환경 : Julia v1.8.3, DuckDB v0.6.0, DataFrames v1.3.6

KOSPI DATA (2012 ~ 2022) :

KOSPI관련 분석 내용은 아래 링크를 참조

KOSPI 수익률의 표준편차는? #1 https://sine-qua-none.tistory.com/14
KOSPI수익률의 표준편차는? #2 https://sine-qua-none.tistory.com/15
KOSPI 수익률의 표준편차는? #3 (로그수익률) https://sine-qua-none.tistory.com/15
KOSPI 수익률의 표준편차는? #4(로그수익률) https://sine-qua-none.tistory.com/20
KOSPI수익률의 분포는 어떤 모양일까? #1 https://sine-qua-none.tistory.com/24
KOSPI수익률의 분포는 어떤 모양일까? #2 https://sine-qua-none.tistory.com/25

DuckDB와 DataFrames를 같이 사용하는 방법을 포함함

kospi-analysis

DuckDB 사용법 및 KOSPI 주가지수 분포 분석¶

DuckDB :

DBInterface :

https://github.com/JuliaDatabases/DBInterface.jl

Table Create From Dataframe :

https://duckdb.org/docs/guides/python/import_pandas.html

Curve Fitting

https://morioh.com/p/466c5c58dd1d

In [1]:

using DataFrames
using CSV
using Statistics
using Pipe
using Chain
using Dates
using DuckDB
using BenchmarkTools
using Plots
using LsqFit
using Distributions
using StatsPlots
import MathTeXEngine as ML
using PrettyPrint:pprintln

In [2]:

# ENV["LINES"] and ENV["COLUMNS"]
ENV["COLUMNS"] = 120
DP = display
# 챠트 폰트
# default(fontfamily="")

Out[2]:

display (generic function with 32 methods)

DuckDB 사용법¶

In [3]:

data_file = "./data/kospi_index_2012_2022.csv"

Out[3]:

"./data/kospi_index_2012_2022.csv"

In [4]:

df = CSV.File(data_file) |> DataFrame
DP(first(df,3))
@chain df begin
    transform!(
        [:open,:close,:high,:low] .=> x->parse.(Float64,replace.(x,","=>"")) ,
        [:volume] .=> x-> begin 
            # 마지막 1개의 chracter이므로 문자열 비교가 아닌 chracter 비교
            map(y-> y[end] == 'K' ? round(Int,parse(Float64,y[1:end-1]) * 1000) : 
                round(Int,parse(Float64,y[1:end-1]) * 10000),x)
            end,
        renamecols=false)
end
df

3 rows × 7 columns

	date	close	open	high	low	volume	return
	Date	String15	String15	String15	String15	String7	Float64
1	2022-12-27	2,330.39	2,327.52	2,335.99	2,322.27	154.50K	0.0057
2	2022-12-26	2,317.14	2,312.54	2,321.92	2,304.20	427.84K	0.0015
3	2022-12-23	2,313.69	2,325.86	2,333.08	2,311.90	366.99M	-0.0183

Out[4]:

2,708 rows × 7 columns

	date	close	open	high	low	volume	return
	Date	Float64	Float64	Float64	Float64	Int64	Float64
1	2022-12-27	2330.39	2327.52	2335.99	2322.27	154500	0.0057
2	2022-12-26	2317.14	2312.54	2321.92	2304.2	427840	0.0015
3	2022-12-23	2313.69	2325.86	2333.08	2311.9	3669900	-0.0183
4	2022-12-22	2356.73	2340.0	2356.73	2335.75	5530500	0.0119
5	2022-12-21	2328.95	2346.39	2347.0	2325.78	3297200	-0.0019
6	2022-12-20	2333.29	2344.73	2353.86	2324.66	3587700	-0.008
7	2022-12-19	2352.17	2350.78	2358.76	2342.28	3239900	-0.0033
8	2022-12-16	2360.02	2329.75	2360.44	2326.83	4141700	-0.0004
9	2022-12-15	2360.97	2383.83	2392.11	2360.95	3753900	-0.016
10	2022-12-14	2399.25	2380.81	2400.18	2379.44	4098000	0.0113
11	2022-12-13	2372.4	2385.05	2388.27	2364.87	4475600	-0.0003
12	2022-12-12	2373.02	2373.58	2381.87	2368.47	4992200	-0.0067
13	2022-12-09	2389.04	2382.73	2390.08	2367.25	3156700	0.0076
14	2022-12-08	2371.08	2386.9	2387.95	2357.2	3519400	-0.0049
15	2022-12-07	2382.81	2385.87	2394.88	2377.98	3325900	-0.0043
16	2022-12-06	2393.16	2397.7	2416.88	2390.2	3686400	-0.0108
17	2022-12-05	2419.32	2442.17	2442.22	2413.05	3855900	-0.0062
18	2022-12-02	2434.33	2471.5	2471.5	2434.33	4688500	-0.0184
19	2022-12-01	2479.84	2501.43	2501.43	2474.33	4913800	0.003
20	2022-11-30	2472.53	2424.44	2472.53	2421.42	5941300	0.0161
21	2022-11-29	2433.39	2405.54	2433.87	2401.1	5501700	0.0104
22	2022-11-28	2408.27	2425.05	2425.65	2401.95	3505000	-0.0121
23	2022-11-25	2437.86	2442.21	2449.66	2433.57	4383900	-0.0014
24	2022-11-24	2441.33	2437.51	2441.33	2428.12	4811800	0.0096
25	2022-11-23	2418.01	2424.36	2427.28	2407.58	4747900	0.0053
26	2022-11-22	2405.27	2405.96	2426.4	2401.5	5391700	-0.0059
27	2022-11-21	2419.5	2446.05	2448.14	2409.36	5445300	-0.0102
28	2022-11-18	2444.48	2448.13	2471.87	2442.87	5895900	0.0006
29	2022-11-17	2442.9	2466.5	2467.39	2442.9	9145200	-0.0139
30	2022-11-16	2477.45	2487.0	2487.0	2446.79	6578300	-0.0012
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮

In [5]:

describe(df,:eltype)

Out[5]:

7 rows × 2 columns

	variable	eltype
	Symbol	DataType
1	date	Date
2	close	Float64
3	open	Float64
4	high	Float64
5	low	Float64
6	volume	Int64
7	return	Float64

In [6]:

# @btime
df[ DateTime("2022-04-29") .>= df.date .>= DateTime("2022-04-18"),:]

Out[6]:

10 rows × 7 columns

	date	close	open	high	low	volume	return
	Date	Float64	Float64	Float64	Float64	Int64	Float64
1	2022-04-29	2695.05	2669.18	2696.1	2664.06	962400	0.0103
2	2022-04-28	2667.49	2656.54	2667.49	2638.37	8991700	0.0108
3	2022-04-27	2639.06	2630.58	2641.82	2615.5	10700	-0.011
4	2022-04-26	2668.31	2674.0	2678.05	2663.83	8899400	0.0042
5	2022-04-25	2657.13	2676.67	2680.35	2657.04	988350	-0.0176
6	2022-04-22	2704.71	2704.72	2708.58	2690.48	12400	-0.0086
7	2022-04-21	2728.21	2725.71	2737.54	2725.04	10000	0.0035
8	2022-04-20	2718.69	2718.49	2724.46	2702.84	17400	-0.0001
9	2022-04-19	2718.89	2707.76	2723.98	2705.32	12600	0.0095
10	2022-04-18	2693.21	2685.04	2701.11	2681.37	10200	-0.0011

In [7]:

# @btime
filter(:date => x-> DateTime("2022-04-29") >= x >= DateTime("2022-04-18"),df)

Out[7]:

10 rows × 7 columns

	date	close	open	high	low	volume	return
	Date	Float64	Float64	Float64	Float64	Int64	Float64
1	2022-04-29	2695.05	2669.18	2696.1	2664.06	962400	0.0103
2	2022-04-28	2667.49	2656.54	2667.49	2638.37	8991700	0.0108
3	2022-04-27	2639.06	2630.58	2641.82	2615.5	10700	-0.011
4	2022-04-26	2668.31	2674.0	2678.05	2663.83	8899400	0.0042
5	2022-04-25	2657.13	2676.67	2680.35	2657.04	988350	-0.0176
6	2022-04-22	2704.71	2704.72	2708.58	2690.48	12400	-0.0086
7	2022-04-21	2728.21	2725.71	2737.54	2725.04	10000	0.0035
8	2022-04-20	2718.69	2718.49	2724.46	2702.84	17400	-0.0001
9	2022-04-19	2718.89	2707.76	2723.98	2705.32	12600	0.0095
10	2022-04-18	2693.21	2685.04	2701.11	2681.37	10200	-0.0011

In [8]:

# @btime 
df2 = @chain df begin
    filter(:date =>  >=(DateTime("2022-04-18")),_)
    filter(:date =>  <=(DateTime("2022-04-29")),_)
end

Out[8]:

10 rows × 7 columns

	date	close	open	high	low	volume	return
	Date	Float64	Float64	Float64	Float64	Int64	Float64
1	2022-04-29	2695.05	2669.18	2696.1	2664.06	962400	0.0103
2	2022-04-28	2667.49	2656.54	2667.49	2638.37	8991700	0.0108
3	2022-04-27	2639.06	2630.58	2641.82	2615.5	10700	-0.011
4	2022-04-26	2668.31	2674.0	2678.05	2663.83	8899400	0.0042
5	2022-04-25	2657.13	2676.67	2680.35	2657.04	988350	-0.0176
6	2022-04-22	2704.71	2704.72	2708.58	2690.48	12400	-0.0086
7	2022-04-21	2728.21	2725.71	2737.54	2725.04	10000	0.0035
8	2022-04-20	2718.69	2718.49	2724.46	2702.84	17400	-0.0001
9	2022-04-19	2718.89	2707.76	2723.98	2705.32	12600	0.0095
10	2022-04-18	2693.21	2685.04	2701.11	2681.37	10200	-0.0011

In [9]:

for r in eachrow(df[1:5,:])
    @show r.open, r.close, r.high, r.low, r.volume, r.return
end

(r.open, r.close, r.high, r.low, r.volume, r.return) = (2327.52, 2330.39, 2335.99, 2322.27, 154500, 0.0057)
(r.open, r.close, r.high, r.low, r.volume, r.return) = (2312.54, 2317.14, 2321.92, 2304.2, 427840, 0.0015)
(r.open, r.close, r.high, r.low, r.volume, r.return) = (2325.86, 2313.69, 2333.08, 2311.9, 3669900, -0.0183)
(r.open, r.close, r.high, r.low, r.volume, r.return) = (2340.0, 2356.73, 2356.73, 2335.75, 5530500, 0.0119)
(r.open, r.close, r.high, r.low, r.volume, r.return) = (2346.39, 2328.95, 2347.0, 2325.78, 3297200, -0.0019)

DuckDB¶

In [10]:

# db = DuckDB.open(":memory:")
# con = DuckDB.connect(db)
con = DBInterface.connect(DuckDB.DB, ":memory:")

Out[10]:

DuckDB.DB(":memory:")

In [11]:

DBInterface.execute(con,
    """
    DESCRIBE
    SELECT *
    FROM '$(data_file)'
    LIMIT 100
    """)

Out[11]:

7×6 DataFrame
 Row │ column_name  column_type  null     key      default  extra   
     │ String?      String?      String?  String?  String?  String? 
─────┼──────────────────────────────────────────────────────────────
   1 │ date         DATE         YES      missing  missing  missing 
   2 │ close        VARCHAR      YES      missing  missing  missing 
   3 │ open         VARCHAR      YES      missing  missing  missing 
   4 │ high         VARCHAR      YES      missing  missing  missing 
   5 │ low          VARCHAR      YES      missing  missing  missing 
   6 │ volume       VARCHAR      YES      missing  missing  missing 
   7 │ return       VARCHAR      YES      missing  missing  missing

DataFrame에서 table을 생성하고 데이터를 입력¶

In [12]:

# df 를 mydf로 등록
DuckDB.register_data_frame(con, df, "mydf")

# create the table "kospi" from the DataFrame "df"
DBInterface.execute(con,"CREATE TABLE kospi AS SELECT * FROM mydf")

# # insert into the table "my_table" from the DataFrame "my_df"
# DBInterface.execute(con, "INSERT INTO kospi SELECT * FROM df")

Out[12]:

1×1 DataFrame
 Row │ Count  
     │ Int64? 
─────┼────────
   1 │   2708

In [13]:

DBInterface.execute(con,
"""
    SELECT * FROM kospi
""")

Out[13]:

2708×7 DataFrame
  Row │ date        close     open      high      low       volume   return   
      │ Date?       Float64?  Float64?  Float64?  Float64?  Int64?   Float64? 
──────┼───────────────────────────────────────────────────────────────────────
    1 │ 2022-12-27   2330.39   2327.52   2335.99   2322.27   154500    0.0057
    2 │ 2022-12-26   2317.14   2312.54   2321.92   2304.2    427840    0.0015
    3 │ 2022-12-23   2313.69   2325.86   2333.08   2311.9   3669900   -0.0183
    4 │ 2022-12-22   2356.73   2340.0    2356.73   2335.75  5530500    0.0119
    5 │ 2022-12-21   2328.95   2346.39   2347.0    2325.78  3297200   -0.0019
    6 │ 2022-12-20   2333.29   2344.73   2353.86   2324.66  3587700   -0.008
    7 │ 2022-12-19   2352.17   2350.78   2358.76   2342.28  3239900   -0.0033
    8 │ 2022-12-16   2360.02   2329.75   2360.44   2326.83  4141700   -0.0004
    9 │ 2022-12-15   2360.97   2383.83   2392.11   2360.95  3753900   -0.016
   10 │ 2022-12-14   2399.25   2380.81   2400.18   2379.44  4098000    0.0113
   11 │ 2022-12-13   2372.4    2385.05   2388.27   2364.87  4475600   -0.0003
  ⋮   │     ⋮          ⋮         ⋮         ⋮         ⋮         ⋮        ⋮
 2699 │ 2012-01-13   1875.68   1865.72   1881.84   1861.53  4750300    0.006
 2700 │ 2012-01-12   1864.57   1853.1    1864.57   1837.96  4763400    0.0103
 2701 │ 2012-01-11   1845.55   1857.54   1857.82   1843.12  4479600   -0.0041
 2702 │ 2012-01-10   1853.22   1841.13   1859.55   1840.47  3886400    0.0146
 2703 │ 2012-01-09   1826.49   1832.04   1832.04   1810.48  3955100   -0.009
 2704 │ 2012-01-06   1843.14   1867.12   1867.12   1824.29  4726800   -0.0111
 2705 │ 2012-01-05   1863.74   1869.42   1875.97   1860.57  5337700   -0.0013
 2706 │ 2012-01-04   1866.22   1883.48   1884.69   1866.22  4945000   -0.0049
 2707 │ 2012-01-03   1875.41   1846.56   1875.41   1846.56  4434700    0.0269
 2708 │ 2012-01-02   1826.37   1831.69   1837.81   1814.55  3233600    0.0003
                                                             2687 rows omitted

In [14]:

stmt = DBInterface.prepare(con,
    """
    SELECT * FROM kospi
    WHERE date BETWEEN '2022-04-18' AND '2022-04-29'
"""
)

Out[14]:

DuckDB.Stmt(DuckDB.Connection(":memory:"), Ptr{Nothing} @0x000000000dab2230, "    SELECT * FROM kospi\n    WHERE date BETWEEN '2022-04-18' AND '2022-04-29'\n")

In [15]:

# @btime 
DBInterface.execute(stmt)

Out[15]:

10×7 DataFrame
 Row │ date        close     open      high      low       volume   return   
     │ Date?       Float64?  Float64?  Float64?  Float64?  Int64?   Float64? 
─────┼───────────────────────────────────────────────────────────────────────
   1 │ 2022-04-29   2695.05   2669.18   2696.1    2664.06   962400    0.0103
   2 │ 2022-04-28   2667.49   2656.54   2667.49   2638.37  8991700    0.0108
   3 │ 2022-04-27   2639.06   2630.58   2641.82   2615.5     10700   -0.011
   4 │ 2022-04-26   2668.31   2674.0    2678.05   2663.83  8899400    0.0042
   5 │ 2022-04-25   2657.13   2676.67   2680.35   2657.04   988350   -0.0176
   6 │ 2022-04-22   2704.71   2704.72   2708.58   2690.48    12400   -0.0086
   7 │ 2022-04-21   2728.21   2725.71   2737.54   2725.04    10000    0.0035
   8 │ 2022-04-20   2718.69   2718.49   2724.46   2702.84    17400   -0.0001
   9 │ 2022-04-19   2718.89   2707.76   2723.98   2705.32    12600    0.0095
  10 │ 2022-04-18   2693.21   2685.04   2701.11   2681.37    10200   -0.0011

In [16]:

tbl = DBInterface.execute(stmt)

Out[16]:

10×7 DataFrame
 Row │ date        close     open      high      low       volume   return   
     │ Date?       Float64?  Float64?  Float64?  Float64?  Int64?   Float64? 
─────┼───────────────────────────────────────────────────────────────────────
   1 │ 2022-04-29   2695.05   2669.18   2696.1    2664.06   962400    0.0103
   2 │ 2022-04-28   2667.49   2656.54   2667.49   2638.37  8991700    0.0108
   3 │ 2022-04-27   2639.06   2630.58   2641.82   2615.5     10700   -0.011
   4 │ 2022-04-26   2668.31   2674.0    2678.05   2663.83  8899400    0.0042
   5 │ 2022-04-25   2657.13   2676.67   2680.35   2657.04   988350   -0.0176
   6 │ 2022-04-22   2704.71   2704.72   2708.58   2690.48    12400   -0.0086
   7 │ 2022-04-21   2728.21   2725.71   2737.54   2725.04    10000    0.0035
   8 │ 2022-04-20   2718.69   2718.49   2724.46   2702.84    17400   -0.0001
   9 │ 2022-04-19   2718.89   2707.76   2723.98   2705.32    12600    0.0095
  10 │ 2022-04-18   2693.21   2685.04   2701.11   2681.37    10200   -0.0011

In [17]:

DuckDB.toDataFrame(tbl)
# tbl.df

Out[17]:

10 rows × 7 columns

	date	close	open	high	low	volume	return
	Date?	Float64?	Float64?	Float64?	Float64?	Int64?	Float64?
1	2022-04-29	2695.05	2669.18	2696.1	2664.06	962400	0.0103
2	2022-04-28	2667.49	2656.54	2667.49	2638.37	8991700	0.0108
3	2022-04-27	2639.06	2630.58	2641.82	2615.5	10700	-0.011
4	2022-04-26	2668.31	2674.0	2678.05	2663.83	8899400	0.0042
5	2022-04-25	2657.13	2676.67	2680.35	2657.04	988350	-0.0176
6	2022-04-22	2704.71	2704.72	2708.58	2690.48	12400	-0.0086
7	2022-04-21	2728.21	2725.71	2737.54	2725.04	10000	0.0035
8	2022-04-20	2718.69	2718.49	2724.46	2702.84	17400	-0.0001
9	2022-04-19	2718.89	2707.76	2723.98	2705.32	12600	0.0095
10	2022-04-18	2693.21	2685.04	2701.11	2681.37	10200	-0.0011

In [18]:

DBInterface.close!(stmt)

In [19]:

# DuckDB.appendDataFrame(df,con,"kospi")

In [20]:

DBInterface.execute(con,
"""
    INSERT INTO kospi
    VALUES('2022-12-28', 10.0, 11.0, 12.0, 13.0, 10000, 0.1234)
""")

Out[20]:

1×1 DataFrame
 Row │ Count  
     │ Int64? 
─────┼────────
   1 │      1

In [21]:

DBInterface.execute(con, "SELECT * FROM kospi")

Out[21]:

2709×7 DataFrame
  Row │ date        close     open      high      low       volume   return   
      │ Date?       Float64?  Float64?  Float64?  Float64?  Int64?   Float64? 
──────┼───────────────────────────────────────────────────────────────────────
    1 │ 2022-12-27   2330.39   2327.52   2335.99   2322.27   154500    0.0057
    2 │ 2022-12-26   2317.14   2312.54   2321.92   2304.2    427840    0.0015
    3 │ 2022-12-23   2313.69   2325.86   2333.08   2311.9   3669900   -0.0183
    4 │ 2022-12-22   2356.73   2340.0    2356.73   2335.75  5530500    0.0119
    5 │ 2022-12-21   2328.95   2346.39   2347.0    2325.78  3297200   -0.0019
    6 │ 2022-12-20   2333.29   2344.73   2353.86   2324.66  3587700   -0.008
    7 │ 2022-12-19   2352.17   2350.78   2358.76   2342.28  3239900   -0.0033
    8 │ 2022-12-16   2360.02   2329.75   2360.44   2326.83  4141700   -0.0004
    9 │ 2022-12-15   2360.97   2383.83   2392.11   2360.95  3753900   -0.016
   10 │ 2022-12-14   2399.25   2380.81   2400.18   2379.44  4098000    0.0113
   11 │ 2022-12-13   2372.4    2385.05   2388.27   2364.87  4475600   -0.0003
  ⋮   │     ⋮          ⋮         ⋮         ⋮         ⋮         ⋮        ⋮
 2700 │ 2012-01-12   1864.57   1853.1    1864.57   1837.96  4763400    0.0103
 2701 │ 2012-01-11   1845.55   1857.54   1857.82   1843.12  4479600   -0.0041
 2702 │ 2012-01-10   1853.22   1841.13   1859.55   1840.47  3886400    0.0146
 2703 │ 2012-01-09   1826.49   1832.04   1832.04   1810.48  3955100   -0.009
 2704 │ 2012-01-06   1843.14   1867.12   1867.12   1824.29  4726800   -0.0111
 2705 │ 2012-01-05   1863.74   1869.42   1875.97   1860.57  5337700   -0.0013
 2706 │ 2012-01-04   1866.22   1883.48   1884.69   1866.22  4945000   -0.0049
 2707 │ 2012-01-03   1875.41   1846.56   1875.41   1846.56  4434700    0.0269
 2708 │ 2012-01-02   1826.37   1831.69   1837.81   1814.55  3233600    0.0003
 2709 │ 2022-12-28     10.0      11.0      12.0      13.0     10000    0.1234
                                                             2688 rows omitted

In [22]:

DBInterface.execute(con, "DELETE FROM kospi WHERE date = '2022-12-28'")

Out[22]:

1×1 DataFrame
 Row │ Count  
     │ Int64? 
─────┼────────
   1 │      1

In [23]:

DBInterface.execute(con, "SELECT * FROM kospi")

Out[23]:

2708×7 DataFrame
  Row │ date        close     open      high      low       volume   return   
      │ Date?       Float64?  Float64?  Float64?  Float64?  Int64?   Float64? 
──────┼───────────────────────────────────────────────────────────────────────
    1 │ 2022-12-27   2330.39   2327.52   2335.99   2322.27   154500    0.0057
    2 │ 2022-12-26   2317.14   2312.54   2321.92   2304.2    427840    0.0015
    3 │ 2022-12-23   2313.69   2325.86   2333.08   2311.9   3669900   -0.0183
    4 │ 2022-12-22   2356.73   2340.0    2356.73   2335.75  5530500    0.0119
    5 │ 2022-12-21   2328.95   2346.39   2347.0    2325.78  3297200   -0.0019
    6 │ 2022-12-20   2333.29   2344.73   2353.86   2324.66  3587700   -0.008
    7 │ 2022-12-19   2352.17   2350.78   2358.76   2342.28  3239900   -0.0033
    8 │ 2022-12-16   2360.02   2329.75   2360.44   2326.83  4141700   -0.0004
    9 │ 2022-12-15   2360.97   2383.83   2392.11   2360.95  3753900   -0.016
   10 │ 2022-12-14   2399.25   2380.81   2400.18   2379.44  4098000    0.0113
   11 │ 2022-12-13   2372.4    2385.05   2388.27   2364.87  4475600   -0.0003
  ⋮   │     ⋮          ⋮         ⋮         ⋮         ⋮         ⋮        ⋮
 2699 │ 2012-01-13   1875.68   1865.72   1881.84   1861.53  4750300    0.006
 2700 │ 2012-01-12   1864.57   1853.1    1864.57   1837.96  4763400    0.0103
 2701 │ 2012-01-11   1845.55   1857.54   1857.82   1843.12  4479600   -0.0041
 2702 │ 2012-01-10   1853.22   1841.13   1859.55   1840.47  3886400    0.0146
 2703 │ 2012-01-09   1826.49   1832.04   1832.04   1810.48  3955100   -0.009
 2704 │ 2012-01-06   1843.14   1867.12   1867.12   1824.29  4726800   -0.0111
 2705 │ 2012-01-05   1863.74   1869.42   1875.97   1860.57  5337700   -0.0013
 2706 │ 2012-01-04   1866.22   1883.48   1884.69   1866.22  4945000   -0.0049
 2707 │ 2012-01-03   1875.41   1846.56   1875.41   1846.56  4434700    0.0269
 2708 │ 2012-01-02   1826.37   1831.69   1837.81   1814.55  3233600    0.0003
                                                             2687 rows omitted

In [24]:

DBInterface.execute(con, "COPY (SELECT * FROM kospi) TO './data/kospi.parquet' (FORMAT 'parquet');")

Out[24]:

1×1 DataFrame
 Row │ Count  
     │ Int64? 
─────┼────────
   1 │   2708

In [25]:

DBInterface.close!(con)

Load parquet using DuckDB¶

In [26]:

con = DBInterface.connect(DuckDB.DB, ":memory:")

Out[26]:

DuckDB.DB(":memory:")

In [27]:

DBInterface.execute(con,
"""
    SELECT * 
    FROM "./data/kospi.parquet"
""")

Out[27]:

2708×7 DataFrame
  Row │ date        close     open      high      low       volume   return   
      │ Date?       Float64?  Float64?  Float64?  Float64?  Int64?   Float64? 
──────┼───────────────────────────────────────────────────────────────────────
    1 │ 2022-12-27   2330.39   2327.52   2335.99   2322.27   154500    0.0057
    2 │ 2022-12-26   2317.14   2312.54   2321.92   2304.2    427840    0.0015
    3 │ 2022-12-23   2313.69   2325.86   2333.08   2311.9   3669900   -0.0183
    4 │ 2022-12-22   2356.73   2340.0    2356.73   2335.75  5530500    0.0119
    5 │ 2022-12-21   2328.95   2346.39   2347.0    2325.78  3297200   -0.0019
    6 │ 2022-12-20   2333.29   2344.73   2353.86   2324.66  3587700   -0.008
    7 │ 2022-12-19   2352.17   2350.78   2358.76   2342.28  3239900   -0.0033
    8 │ 2022-12-16   2360.02   2329.75   2360.44   2326.83  4141700   -0.0004
    9 │ 2022-12-15   2360.97   2383.83   2392.11   2360.95  3753900   -0.016
   10 │ 2022-12-14   2399.25   2380.81   2400.18   2379.44  4098000    0.0113
   11 │ 2022-12-13   2372.4    2385.05   2388.27   2364.87  4475600   -0.0003
  ⋮   │     ⋮          ⋮         ⋮         ⋮         ⋮         ⋮        ⋮
 2699 │ 2012-01-13   1875.68   1865.72   1881.84   1861.53  4750300    0.006
 2700 │ 2012-01-12   1864.57   1853.1    1864.57   1837.96  4763400    0.0103
 2701 │ 2012-01-11   1845.55   1857.54   1857.82   1843.12  4479600   -0.0041
 2702 │ 2012-01-10   1853.22   1841.13   1859.55   1840.47  3886400    0.0146
 2703 │ 2012-01-09   1826.49   1832.04   1832.04   1810.48  3955100   -0.009
 2704 │ 2012-01-06   1843.14   1867.12   1867.12   1824.29  4726800   -0.0111
 2705 │ 2012-01-05   1863.74   1869.42   1875.97   1860.57  5337700   -0.0013
 2706 │ 2012-01-04   1866.22   1883.48   1884.69   1866.22  4945000   -0.0049
 2707 │ 2012-01-03   1875.41   1846.56   1875.41   1846.56  4434700    0.0269
 2708 │ 2012-01-02   1826.37   1831.69   1837.81   1814.55  3233600    0.0003
                                                             2687 rows omitted

In [28]:

DBInterface.close!(con)

In [29]:

con = DBInterface.connect(DuckDB.DB, ":memory:")

Out[29]:

DuckDB.DB(":memory:")

In [30]:

DBInterface.execute(con,
    """CREATE TABLE kospi AS SELECT * FROM "./data/kospi.parquet" """
)

Out[30]:

1×1 DataFrame
 Row │ Count  
     │ Int64? 
─────┼────────
   1 │   2708

In [31]:

tbl = DBInterface.execute(con,
"""
    SELECT * 
    FROM kospi
""")

Out[31]:

2708×7 DataFrame
  Row │ date        close     open      high      low       volume   return   
      │ Date?       Float64?  Float64?  Float64?  Float64?  Int64?   Float64? 
──────┼───────────────────────────────────────────────────────────────────────
    1 │ 2022-12-27   2330.39   2327.52   2335.99   2322.27   154500    0.0057
    2 │ 2022-12-26   2317.14   2312.54   2321.92   2304.2    427840    0.0015
    3 │ 2022-12-23   2313.69   2325.86   2333.08   2311.9   3669900   -0.0183
    4 │ 2022-12-22   2356.73   2340.0    2356.73   2335.75  5530500    0.0119
    5 │ 2022-12-21   2328.95   2346.39   2347.0    2325.78  3297200   -0.0019
    6 │ 2022-12-20   2333.29   2344.73   2353.86   2324.66  3587700   -0.008
    7 │ 2022-12-19   2352.17   2350.78   2358.76   2342.28  3239900   -0.0033
    8 │ 2022-12-16   2360.02   2329.75   2360.44   2326.83  4141700   -0.0004
    9 │ 2022-12-15   2360.97   2383.83   2392.11   2360.95  3753900   -0.016
   10 │ 2022-12-14   2399.25   2380.81   2400.18   2379.44  4098000    0.0113
   11 │ 2022-12-13   2372.4    2385.05   2388.27   2364.87  4475600   -0.0003
  ⋮   │     ⋮          ⋮         ⋮         ⋮         ⋮         ⋮        ⋮
 2699 │ 2012-01-13   1875.68   1865.72   1881.84   1861.53  4750300    0.006
 2700 │ 2012-01-12   1864.57   1853.1    1864.57   1837.96  4763400    0.0103
 2701 │ 2012-01-11   1845.55   1857.54   1857.82   1843.12  4479600   -0.0041
 2702 │ 2012-01-10   1853.22   1841.13   1859.55   1840.47  3886400    0.0146
 2703 │ 2012-01-09   1826.49   1832.04   1832.04   1810.48  3955100   -0.009
 2704 │ 2012-01-06   1843.14   1867.12   1867.12   1824.29  4726800   -0.0111
 2705 │ 2012-01-05   1863.74   1869.42   1875.97   1860.57  5337700   -0.0013
 2706 │ 2012-01-04   1866.22   1883.48   1884.69   1866.22  4945000   -0.0049
 2707 │ 2012-01-03   1875.41   1846.56   1875.41   1846.56  4434700    0.0269
 2708 │ 2012-01-02   1826.37   1831.69   1837.81   1814.55  3233600    0.0003
                                                             2687 rows omitted

In [32]:

df = DuckDB.toDataFrame(tbl)
df[1:3,:]

Out[32]:

3 rows × 7 columns

	date	close	open	high	low	volume	return
	Date?	Float64?	Float64?	Float64?	Float64?	Int64?	Float64?
1	2022-12-27	2330.39	2327.52	2335.99	2322.27	154500	0.0057
2	2022-12-26	2317.14	2312.54	2321.92	2304.2	427840	0.0015
3	2022-12-23	2313.69	2325.86	2333.08	2311.9	3669900	-0.0183

DataFrame에서 특정 column 삭제 방법¶

select!(df,Not([:r02]))

시간에 따른 수익률¶

https://sine-qua-none.tistory.com/15

In [33]:

T = 30
select!(df,1:7)
for t in 1:T
    df[!,Symbol("r"*lpad(t,3,"0"))] = map(i->try log(df.close[i]/df.close[i+t]) catch e missing  end, 1:size(df,1)) 
end
describe(df,:eltype)
dropmissing!(df)
last(df,10)

Out[33]:

10 rows × 37 columns (omitted printing of 26 columns)

	date	close	open	high	low	volume	return	r001	r002	r003	r004
	Date	Float64	Float64	Float64	Float64	Int64	Float64	Float64	Float64	Float64	Float64
1	2012-02-28	2003.69	1995.93	2006.26	1992.66	6079300	0.0063	0.0062731	-0.00805257	-0.00204911	-0.0123801
2	2012-02-27	1991.16	2013.61	2013.69	1987.74	6360100	-0.0142	-0.0143257	-0.00832221	-0.0186532	-0.0164769
3	2012-02-24	2019.89	2010.6	2019.9	1998.39	7179100	0.006	0.00600346	-0.00432749	-0.00215127	-0.00247726
4	2012-02-23	2007.8	2016.46	2016.46	2001.25	6901200	-0.0103	-0.010331	-0.00815473	-0.00848072	-0.00777426
5	2012-02-22	2028.65	2018.07	2028.93	2015.3	8837400	0.0022	0.00217623	0.00185023	0.00255669	0.0154992
6	2012-02-21	2024.24	2022.05	2030.46	2007.46	7090200	-0.0003	-0.000325995	0.000380462	0.013323	-0.000533391
7	2012-02-20	2024.9	2041.51	2047.43	2024.59	7339200	0.0007	0.000706457	0.0136489	-0.000207396	0.011054
8	2012-02-17	2023.47	2025.56	2031.4	2019.79	7310900	0.013	0.0129425	-0.000913853	0.0103475	0.00880079
9	2012-02-16	1997.45	2005.37	2012.44	1995.99	6966900	-0.0138	-0.0138563	-0.00259494	-0.0041417	0.00187414
10	2012-02-15	2025.32	2012.0	2026.75	2009.68	6814700	0.0113	0.0112614	0.00971464	0.0157305	0.00529712

In [34]:

DuckDB.register_data_frame(con,df,"mydf")

In [35]:

df2 = DBInterface.execute(con,
"""
    SELECT * from mydf
    --WHERE date BETWEEN '2022-04-14' AND '2022-04-29'
"""
).df[1:3,:]

Out[35]:

3 rows × 37 columns (omitted printing of 26 columns)

	date	close	open	high	low	volume	return	r001	r002	r003	r004
	Date?	Float64?	Float64?	Float64?	Float64?	Int64?	Float64?	Float64?	Float64?	Float64?	Float64?
1	2022-12-27	2330.39	2327.52	2335.99	2322.27	154500	0.0057	0.00570197	0.00719198	-0.0112394	0.000618113
2	2022-12-26	2317.14	2312.54	2321.92	2304.2	427840	0.0015	0.00149001	-0.0169414	-0.00508386	-0.00694562
3	2022-12-23	2313.69	2325.86	2333.08	2311.9	3669900	-0.0183	-0.0184314	-0.00657387	-0.00843564	-0.0164947

수익률의 분포¶

시간에 따른 수익률의 분포$f(t)$는 $N(0,\sigma_{1}\sqrt{t})$ 인 정규분포를 따른다고 모델링 하고 맞는지 살펴보자\ 여기서 $\sigma_{1}은 1일 수익률의 표준편차$

시간에 따른 수익률의 표준편차¶

In [36]:

stds = Vector{Float64}()
for t in 1:T
    s = Symbol("r"*lpad(t,3,"0"))
    push!(stds,std(df[!,s]))
end
stds

Out[36]:

30-element Vector{Float64}:
 0.009813302121263563
 0.013847351387053404
 0.0174165025070727
 0.020453249357504526
 0.0230023916814406
 0.02526228799874069
 0.02717301743233356
 0.029025990272606158
 0.030760782701878524
 0.03249886065505094
 0.034130906378785214
 0.03561940741563499
 0.03707881163100406
 ⋮
 0.04535414998918937
 0.046623502858969865
 0.047868617940500145
 0.048983952678823266
 0.05005135047409256
 0.05110756129799725
 0.052135935836887436
 0.05314286409024463
 0.054006589724114915
 0.05484988920626446
 0.0556720124490399
 0.056494178052715074

$$ f(x) = a x^b + c\\ a = p[1]\\ b = p[2]\\ c = p[3]\\ $$

In [37]:

@. model(x,p) = p[1]*x^p[2]

Out[37]:

model (generic function with 1 method)

In [38]:

p0 = [0.5, 0.5]
fit = curve_fit(model,1:T,stds,p0; autodiff=:finiteforward)
# fit = curve_fit(model,1:T,stds,p0)

Out[38]:

LsqFit.LsqFitResult{Vector{Float64}, Vector{Float64}, Matrix{Float64}, Vector{Float64}}([0.010013847924725537, 0.5115770633220432], [0.00020054580346197393, 0.0004284676083854914, 0.00014999919202853332, -0.00010153146419331419, -0.00018962210395919235, -0.00021934741041411063, -7.52341438251744e-5, -1.2423951734650412e-5, 5.4742385395479404e-5, 2.319996748500336e-5  …  -0.0003331191234950681, -0.000303608008635492, -0.0002513073202101909, -0.0002113557730322041, -0.00016565830648194307, -0.00011930178976762157, 5.06495982140337e-5, 0.00022249107825247916, 0.0003979499521817101, 0.0005567016369432201], [1.0 0.0; 1.4256077287718654 0.009895243914797902; … ; 5.59924245160073 0.188804155215621; 5.697198531124741 0.19404130754992366], true, Float64[])

In [39]:

param = round.(fit.param,digits=6)

Out[39]:

2-element Vector{Float64}:
 0.010014
 0.511577

Latex string내에 변수사용시 `%`를 붙임¶

예) L"f(x) = %$(param[1])x^{%$(param[2])}"

In [40]:

# stderror(fit; atol, rtol)

In [41]:

#marker=:circle
scatter(1:T,stds,label="std",legend=:bottomright,markersize =1)
plot!(1:T,model(1:T,fit.param),label=ML.L"fit:f(x) = %$(param[1])x^{%$(param[2])}")

Out[41]:

In [42]:

ML.L"f(x) = %$(param[1])x^{%$(param[2])}"

Out[42]:

$f(x) = 0.010014x^{0.511577}$

Coefficient of determination(결정계수) : $R^2$¶

https://www.youtube.com/watch?v=lng4ZgConCM
https://loadtoexcelmaster.tistory.com/entry/%EC%97%91%EC%85%80%EC%97%90%EC%84%9C-%EA%B2%B0%EC%A0%95%EA%B3%84%EC%88%98coefficeint-of-determination-R%C2%B2-%EA%B5%AC%ED%95%98%EA%B8%B0
$R^2$이 1에 가까워 질 수록 fitting이 잘된것임 (0 ~ 1)범위를 가짐
선형회귀모델에서 선형으로 잘 피팅되었는지 나타냄
residuals(잔차) = 샘플값 – 샘플평균 = $X – \bar{X}$ $$ y_i : 관찰값\\ \bar{y} : 관찰값 평균\\ m_i = m(x_i) : 회귀선\\ m(x_i) = a x_i + b\\ SE_{m} = \sum_i \left(y_i – m_i\right)^2\\ SE_{\bar{y}} = \sum_i \left(y_i – \bar{y}\right)^2\\ R^2 = 1 – \frac{SE_{m}}{SE_{\bar{y}}}\\ R^2 = 1 – \frac{MSE(regiduals)}{Var(y_i)}\\ $$
MSE vs $R^2$ : https://vitalflux.com/mean-square-error-r-squared-which-one-to-use/

In [43]:

R²= 1-mse(fit)/var(stds)

Out[43]:

0.9997133613902346

In [44]:

# coefficient
@show coef(fit)
# degree of freedom
@show dof(fit)
# 각 파라미터 p[1], p[2] 의 표준오차
@show stderror(fit)

coef(fit) = [0.010013847924725537, 0.5115770633220432]
dof(fit) = 28
stderror(fit) = [6.112707838441906e-5, 0.002058808906591578]

Out[44]:

2-element Vector{Float64}:
 6.112707838441906e-5
 0.002058808906591578

stderror(fit) 각 파라미터의 표준오차¶

예) p[1], p[2] 즉 a, b 값의 표준오차
표준오차 : https://ballpen.blog/%ED%91%9C%EC%A4%80-%EC%98%A4%EC%B0%A8-%EA%B0%9C%EB%85%90-%EA%B3%84%EC%82%B0-%EB%B0%A9%EB%B2%95/
표준오차 예제 : https://ballpen.blog/%ED%91%9C%EC%A4%80-%EC%98%A4%EC%B0%A8-%EA%B3%84%EC%82%B0-%EC%98%88%EC%A0%9C/
오차의 종류 : https://ballpen.blog/%EC%98%A4%EC%B0%A8-%EA%B3%84%ED%86%B5%EC%98%A4%EC%B0%A8-%EA%B3%BC%EC%8B%A4%EC%98%A4%EC%B0%A8-%EC%9A%B0%EC%97%B0%EC%98%A4%EC%B0%A8%EC%9D%98-%EA%B0%9C%EB%85%90%EA%B3%BC-%EC%98%88%EC%8B%9C/
표준 오차 개념을 이해하는 것은 측정값의 정확도를 올바르게 표기하는데 있어 아주 중요
정확도 : 측정값들이 한쪽으로 몰리는 일이 적은 정도
정밀도 : 측정값들의 퍼짐이 좁은 정도
어느 측정값을 표기하기 위해서는 정밀도 뿐만 아니라 오차의 범위도 제시할 필요가 있습니다. 왜냐하면 정확한 참값을 모르기 때문입니다. 이러한 배경에서 출발한 것이 표준오차가 되겠습니다.
표본 평균의 평균 : 계통오차를 제거하여 참값을 도출하는 방법
표준오차(Standard Error of Mean-SEM, 평균오차) : 표본 평균에 대한 표준편차
- 표본 평균의 평균을 참값으로 간주하고 측정한 측정값들의 표준편차
표본 평균의 평균은 n개의 표본으로부터 구한 평균값이기 때문에 각 표본이 갖는 계통오차들이 서로 상쇄되어 제거된 것으로 볼 수 있어 참값으로 간주
- 상대표준편차($\%RSD$) = $\frac{표준편차}{평균값}\cdot 100$
MSE vs R-Squared($R^2$) https://vitalflux.com/mean-square-error-r-squared-which-one-to-use/

In [45]:

stderror(fit)

Out[45]:

2-element Vector{Float64}:
 6.112707838441906e-5
 0.002058808906591578

In [46]:

ML.L"
t일 수익률의 편차 = a \cdot t^b \;\;\text{로 fitting}\\
f(t) \approx %$(param[1])t^{%$(param[2])}\\
stds[1]=%$(stds[1])\\
a = %$(param[1]) \approx 1일수익율편차 = \sigma = %$(stds[1])\\
b = %$(param[2])\approx \frac{1}{2} \\
t일 수익률편차 = 1일수익률편차 \cdot \sqrt{t}\\
t일 수익률편차(t)= f(t) = \sigma \cdot \sqrt{t}\\
1일수익률편차=f(1) = \sigma\\
"

Out[46]:

$ t일 수익률의 편차 = a \cdot t^b \;\;\text{로 fitting}\\ f(t) \approx 0.010014t^{0.511577}\\ stds[1]=0.009813302121263563\\ a = 0.010014 \approx 1일수익율편차 = \sigma = 0.009813302121263563\\ b = 0.511577\approx \frac{1}{2} \\ t일 수익률편차 = 1일수익률편차 \cdot \sqrt{t}\\ t일 수익률편차(t)= f(t) = \sigma \cdot \sqrt{t}\\ 1일수익률편차=f(1) = \sigma\\ $

수익률의 분포¶

In [47]:

# 1일차 수익률에서 표준편차 σ₁을 구함
dist = Distributions.fit(Normal,df.r001)

Out[47]:

Normal{Float64}(μ=5.659795572039397e-5, σ=0.009811469742922279)

In [48]:

σ₁ = dist.σ

Out[48]:

0.009811469742922279

In [49]:

t_day_return(t) = df[!,"r"*lpad(t,3,"0")]

Out[49]:

t_day_return (generic function with 1 method)

In [50]:

t_return_dist(t,xlim=nothing,ylim=nothing) = begin
    args =[]
     !isnothing(xlim) && push!(args,(:xlim => xlim));
     !isnothing(ylim) && push!(args,(:ylim => ylim));
    dist = Distributions.fit(Normal,t_day_return(t))
    histogram!(t_day_return(t);norm=true,label="$(t) day return observed",alpha=0.3,args...,
        xlabel="Rate of return",ylabel="Probability Density")
    StatsPlots.plot!(dist,lw=2,label="N($(round(dist.μ,digits=5)),$(round(dist.σ,digits=5)))")
    StatsPlots.plot!(Normal(0,σ₁*√t),lw=2,label="Theory : N(0,$(round(σ₁*√t,digits=5)))")
end

Out[50]:

t_return_dist (generic function with 3 methods)

In [51]:

# 이전 plot 연결하지 않고 처음 부터
plot()
t_return_dist(1)

Out[51]:

In [52]:

# 이전 plot 연결하지 않고 처음 부터
plot()
t_return_dist(30)

Out[52]:

t=1,T 의 수익률 분포그래프 겹쳐 보기¶

In [53]:

# 이전 plot 연결하지 않고 처음 부터
plot()
t_return_dist(1,[-0.25,0.25],[-0.5,45.0])
t_return_dist(T,[-0.25,0.25],[-0.5,45.0])

Out[53]:

t=1,…,T 까지 경과시 수익률 분포 변화¶

In [54]:

anim = @animate for t ∈ 1:T
    plot()
    t_return_dist(t,[-0.25,0.25],[-0.5,45.0])
end
gif(anim,"anim_fps3.gif",fps=3)

┌ Info: Saved animation to /home/shpark/julia_dev/finance/anim_fps3.gif
└ @ Plots /home/shpark/.julia/packages/Plots/kYFLA/src/animation.jl:149

Out[54]:

시간경과에 따른 수익율 평균값의 변화 추이¶

In [55]:

pdfs_of_mean = Vector{Float64}()
for t in 1:T
    s = Symbol("r"*lpad(t,3,"0"))
    dist = Distributions.fit(Normal,t_day_return(t))
    # 평균값에서 pdf 값    
    push!(pdfs_of_mean,pdf(dist,dist.μ))
end
pdfs_of_mean

Out[55]:

30-element Vector{Float64}:
 40.66080728518972
 28.81538680076415
 22.91027065979545
 19.50872349960559
 17.34675210778137
 15.79495833488766
 14.684301711345663
 13.74687935317822
 12.971607070312752
 12.277870003483564
 11.690776153312454
 11.202229776818086
 10.761315393678831
  ⋮
  8.797801005622457
  8.558275588838027
  8.335665485057728
  8.145867463989777
  7.9721482558313514
  7.807392414156876
  7.65339261641733
  7.508379407373503
  7.388298139585618
  7.274705421619521
  7.1672779342993325
  7.062971798823522

In [56]:

StatsPlots.scatter(pdfs_of_mean,xlabel="time",markersize =1, 
    ylabel="Probability Density of Mean rate of return")

Out[56]:

In [57]:

@. model2(x,p) = p[1]*x^p[2]

Out[57]:

model2 (generic function with 1 method)

In [58]:

p0 = [0.5, 0.5]
fit2 = curve_fit(model2,1:T,pdfs_of_mean,p0; autodiff=:finiteforward)
param2 = round.(fit2.param,digits=6)

Out[58]:

2-element Vector{Float64}:
 40.692409
 -0.520219

In [59]:

R²= 1-mse(fit2)/var(pdfs_of_mean)

Out[59]:

0.9996898496597619

In [60]:

StatsPlots.scatter(pdfs_of_mean,label="PDF of mean",xlabel="time",
    ylabel="Probability Density of Mean rate of return",markersize =1)
plot!(1:T,model2(1:T,fit2.param),label=ML.L"fit:f(x) = %$(param2[1])x^{%$(param2[2])}")

Out[60]:

In [61]:

DuckDB.register_data_frame(con, df, "kospi_stat")
DBInterface.execute(con, 
    "COPY (SELECT * FROM kospi_stat) TO './data/kospi_stat.parquet' (FORMAT 'parquet');")
DBInterface.close!(con)

[Julia, DuckDB,DataFrames] DuckDB-DataFrames-KOSPI 주가 분포

DuckDB 사용법 및 KOSPI 주가지수 분포 분석¶

DuckDB 사용법¶

DuckDB¶

DataFrame에서 table을 생성하고 데이터를 입력¶

Load parquet using DuckDB¶

DataFrame에서 특정 column 삭제 방법¶

시간에 따른 수익률¶

수익률의 분포¶

시간에 따른 수익률의 표준편차¶

Latex string내에 변수사용시 `%`를 붙임¶

Coefficient of determination(결정계수) : $R^2$¶

stderror(fit) 각 파라미터의 표준오차¶

수익률의 분포¶

t=1,T 의 수익률 분포그래프 겹쳐 보기¶

t=1,…,T 까지 경과시 수익률 분포 변화¶

시간경과에 따른 수익율 평균값의 변화 추이¶

댓글 달기 댓글 취소

DuckDB 사용법 및 KOSPI 주가지수 분포 분석¶

DuckDB 사용법¶

DuckDB¶

DataFrame에서 table을 생성하고 데이터를 입력¶

Load parquet using DuckDB¶

DataFrame에서 특정 column 삭제 방법¶

시간에 따른 수익률¶

수익률의 분포¶

시간에 따른 수익률의 표준편차¶

Latex string내에 변수사용시 %를 붙임¶

Coefficient of determination(결정계수) : $R^2$¶

stderror(fit) 각 파라미터의 표준오차¶

수익률의 분포¶

t=1,T 의 수익률 분포그래프 겹쳐 보기¶

t=1,…,T 까지 경과시 수익률 분포 변화¶

시간경과에 따른 수익율 평균값의 변화 추이¶

댓글 달기 댓글 취소

Latex string내에 변수사용시 `%`를 붙임¶