[TS] (발표) 카카오 주식 시계열분석

Time Series
Author

김보람

Published

December 10, 2023

- 데이터 source: http://data.krx.co.kr/contents/MDC/MDI/mdiLoader/index.cmd?menuId=MDC0201020203

참고 https://velog.io/@isitcake_yes/mlarimastockprediction

kakao <- read.csv("kakaodata_1206.csv", fileEncoding = "ISO-8859-1")
head(kakao)
A data.frame: 6 × 11
ÀÏÀÚ Á... X.ëºñ µî.ô.ü X.Ã.. X.í.. Àú.. X.Å.... X.Å...ë.Ý X.Ã..ÃÑ.. X.óÀåÁÖ.Ä.ö
<chr> <int> <int> <dbl> <int> <int> <int> <int> <dbl> <dbl> <int>
1 2023/12/06 50900 100 0.20 50700 51100 50200 735503 37302792200 2.262484e+13 444495970
2 2023/12/05 50800 0 0.00 50700 51200 50200 1142447 57992282100 2.258040e+13 444495970
3 2023/12/04 50800 1100 2.21 49800 51300 49750 1785113 90624610300 2.258040e+13 444495970
4 2023/12/01 49700 -800 -1.58 50400 50400 49650 1105367 55174771850 2.209145e+13 444495970
5 2023/11/30 50500 0 0.00 50200 50900 50000 1613598 81271347200 2.244705e+13 444495970
6 2023/11/29 50500 -600 -1.17 50800 51300 50100 1284120 65153113600 2.244705e+13 444495970 
colnames(kakao) <- c("일자","종가","대비","등락률","시가","고가","저가","거래량","거래대금","시가총액","상장주식수")
kakao <- kakao[order(kakao$일자),]
rownames(kakao) <- NULL
head(kakao)
A data.frame: 6 × 11
일자 종가 대비 등락률 시가 고가 저가 거래량 거래대금 시가총액 상장주식수
<chr> <int> <int> <dbl> <int> <int> <int> <int> <dbl> <dbl> <int>
1 2023/01/02 52700 -400 -0.75 53600 53800 52400 887667 46979376500 2.347313e+13 445410387
2 2023/01/03 53300 600 1.14 52400 53500 51400 1420569 74588286800 2.374037e+13 445410387
3 2023/01/04 55700 2400 4.50 53200 56000 53100 2241411 123346180300 2.480936e+13 445410387
4 2023/01/05 57700 2000 3.59 55800 58200 55700 3046064 175103778900 2.570018e+13 445410387
5 2023/01/06 57200 -500 -0.87 57200 58000 56500 1420345 81326211100 2.547747e+13 445410387
6 2023/01/09 61100 3900 6.82 58700 61200 58300 3482961 208443993900 2.721457e+13 445410387
  • 시계열 데이터 분석을 하기 위해, 일단.. 일자와 종가만 선택하자.
data <- kakao$종가
data <- ts(data)
head(data)
A Time Series:
  1. 52700
  2. 53300
  3. 55700
  4. 57700
  5. 57200
  6. 61100

  • 해당 데이터는 주식 데이터이기 때문에 중간에 공휴일로 인해 일자가 NA값이 있으므로 ts객체를 통해 그냥 해부림..

  • 데이터가.. 아주 그냥 별로다

forecast::tsdisplay(data)

  • 주식데이터가 평균이 일정하지 않은 비정상성의 특징을 보인다.

  • ARIMA의 d차수가 1이상일 것이다.

  • 계절성분이나 다른 특징은 보이지 않는다.

plot.ts(z)

mean(z)
53663.0434782609 
par(mfrow=c(1,2))
acf(z, lag.max=60)
pacf(z, lag.max=60)

  • ACF가 천천히 줄어들고.. pacr가 첫번째 시차만 살아있고 나머지는 0이다.

  • 시도표를 확인했을 때 계절성분은 없어보이고.. 추세는 조금 있어 보인다.

  • AR(1)모형..?

forecast::ggtsdisplay(z,
        smooth=T)
`geom_smooth()` using formula = 'y ~ x'

  • ACF가 천천히 감소한다. 확률적 추세가 있어보인다.
fUnitRoots::adfTest(z, lags = 1, type = "c")
fUnitRoots::adfTest(z, lags = 30, type = "c")
fUnitRoots::adfTest(z, lags = 60, type = "c")

Title:
 Augmented Dickey-Fuller Test

Test Results:
  PARAMETER:
    Lag Order: 1
  STATISTIC:
    Dickey-Fuller: -1.1594
  P VALUE:
    0.6251 

Description:
 Wed Dec  6 16:27:38 2023 by user: 

Title:
 Augmented Dickey-Fuller Test

Test Results:
  PARAMETER:
    Lag Order: 30
  STATISTIC:
    Dickey-Fuller: -1.2253
  P VALUE:
    0.6005 

Description:
 Wed Dec  6 16:27:38 2023 by user: 

Title:
 Augmented Dickey-Fuller Test

Test Results:
  PARAMETER:
    Lag Order: 60
  STATISTIC:
    Dickey-Fuller: -0.2159
  P VALUE:
    0.9282 

Description:
 Wed Dec  6 16:27:38 2023 by user:
  • 유의확률이 0.05보다 크므로 귀무가설을 기각할 수 없다. 즉 차분이 필요하다.
forecast::ggtsdisplay(diff(z),
        smooth=T)
`geom_smooth()` using formula = 'y ~ x'

  • 0을 중심으로 움직인다.

  • pacf가…감소하는 거 같은데………………………

  • acf가..그림이 잇앙해.ㅐ.

## mean : H0 : mu = 0
t.test(lag_z)

    One Sample t-test

data:  lag_z
t = -0.10283, df = 228, p-value = 0.9182
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -158.4750  142.7545
sample estimates:
mean of x 
-7.860262
  • p-value = 0.9182로 평균이 0이다.

- 차분한 모형(평균f취함)

fit1 <- arima(lag_z, order=c(0,0,1), include.mean = F)
fit1

Call:
arima(x = lag_z, order = c(0, 0, 1), include.mean = F)

Coefficients:
          ma1
      -0.0137
s.e.   0.0646

sigma^2 estimated as 1331943:  log likelihood = -1939.63,  aic = 3883.27

- 원 모형

fit <- arima(z, order=c(0,1,1))
fit

Call:
arima(x = z, order = c(0, 1, 1))

Coefficients:
          ma1
      -0.0137
s.e.   0.0646

sigma^2 estimated as 1331943:  log likelihood = -1939.63,  aic = 3883.27

\(Z_t = ε_t -0.0137ε_t, \hat θ = 0.0137\)

예측

fore_fit <- forecast::forecast(fit)
fore_fit
       Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95
Mar 20       50898.63 49419.59 52377.66 48636.64 53160.62
Apr 20       50898.63 48821.22 52976.03 47721.51 54075.75
May 20       50898.63 48360.19 53437.07 47016.42 54780.84
Jun 20       50898.63 47970.87 53826.38 46421.01 55376.24
Jul 20       50898.63 47627.57 54169.68 45895.98 55901.28
Aug 20       50898.63 47317.03 54480.23 45421.04 56376.22
Sep 20       50898.63 47031.34 54765.92 44984.12 56813.14
Oct 20       50898.63 46765.35 55031.91 44577.32 57219.94
Nov 20       50898.63 46515.47 55281.79 44195.17 57602.09
Dec 20       50898.63 46279.09 55518.17 43833.65 57963.60
Jan 21       50898.63 46054.23 55743.03 43489.76 58307.50
Feb 21       50898.63 45839.35 55957.90 43161.13 58636.12
Mar 21       50898.63 45633.24 56164.02 42845.91 58951.35
Apr 21       50898.63 45434.89 56362.36 42542.57 59254.69
May 21       50898.63 45243.50 56553.76 42249.86 59547.40
Jun 21       50898.63 45058.38 56738.88 41966.73 59830.52
Jul 21       50898.63 44878.94 56918.31 41692.32 60104.94
Aug 21       50898.63 44704.71 57092.55 41425.84 60371.41
Sep 21       50898.63 44535.24 57262.02 41166.66 60630.59
Oct 21       50898.63 44370.17 57427.09 40914.21 60883.05
Nov 21       50898.63 44209.17 57588.09 40667.98 61129.27
Dec 21       50898.63 44051.96 57745.30 40427.55 61369.71
Jan 22       50898.63 43898.27 57898.99 40192.51 61604.75
Feb 22       50898.63 43747.89 58049.37 39962.52 61834.74
plot(fore_fit)

forecast::checkresiduals(fit)

    Ljung-Box test

data:  Residuals from ARIMA(0,1,1)
Q* = 23.178, df = 23, p-value = 0.4504

Model df: 1.   Total lags used: 24

  • 5번째 시차 뭐냐
resid = resid(fit)
forecast::tsdisplay(resid)

# 잔차의 포트맨토 검정 ## H0 : rho1=...=rho_k=0
portes::LjungBox(fit, lags=c(6,12,18,24))
A matrix: 4 × 4 of type dbl
lags statistic df p-value
6 8.728782 5 0.1203836
12 12.770020 11 0.3086222
18 17.077177 17 0.4491493
24 23.178420 23 0.4503932 
## 정규성검정
tseries::jarque.bera.test(resid) ##JB test H0: normal

    Jarque Bera Test

data:  resid
X-squared = 23.774, df = 2, p-value = 6.878e-06
  • 정규분포가 아니넹.
par(mfrow=c(1,2))
hist(resid)

qqnorm(resid, pch=16)
qqline(resid)

## 잔차 검정
astsa::sarima(z, p=0, d=1, q=1)
initial  value 7.051150 
iter   2 value 7.051051
iter   3 value 7.051051
iter   3 value 7.051051
iter   3 value 7.051051
final  value 7.051051 
converged
initial  value 7.051051 
iter   1 value 7.051051
final  value 7.051051 
converged
$fit

Call:
arima(x = xdata, order = c(p, d, q), seasonal = list(order = c(P, D, Q), period = S), 
    xreg = constant, transform.pars = trans, fixed = fixed, optim.control = list(trace = trc, 
        REPORT = 1, reltol = tol))

Coefficients:
          ma1  constant
      -0.0138   -7.9038
s.e.   0.0646   75.2190

sigma^2 estimated as 1331879:  log likelihood = -1939.63,  aic = 3885.26

$degrees_of_freedom
[1] 227

$ttable
         Estimate      SE t.value p.value
ma1       -0.0138  0.0646 -0.2130  0.8315
constant  -7.9038 75.2190 -0.1051  0.9164

$AIC
[1] 16.96618

$AICc
[1] 16.96641

$BIC
[1] 17.01116

fore_fit <- forecast::forecast(fit, 25)
fore_fit
       Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95
Mar 20       50898.63 49419.59 52377.66 48636.64 53160.62
Apr 20       50898.63 48821.22 52976.03 47721.51 54075.75
May 20       50898.63 48360.19 53437.07 47016.42 54780.84
Jun 20       50898.63 47970.87 53826.38 46421.01 55376.24
Jul 20       50898.63 47627.57 54169.68 45895.98 55901.28
Aug 20       50898.63 47317.03 54480.23 45421.04 56376.22
Sep 20       50898.63 47031.34 54765.92 44984.12 56813.14
Oct 20       50898.63 46765.35 55031.91 44577.32 57219.94
Nov 20       50898.63 46515.47 55281.79 44195.17 57602.09
Dec 20       50898.63 46279.09 55518.17 43833.65 57963.60
Jan 21       50898.63 46054.23 55743.03 43489.76 58307.50
Feb 21       50898.63 45839.35 55957.90 43161.13 58636.12
Mar 21       50898.63 45633.24 56164.02 42845.91 58951.35
Apr 21       50898.63 45434.89 56362.36 42542.57 59254.69
May 21       50898.63 45243.50 56553.76 42249.86 59547.40
Jun 21       50898.63 45058.38 56738.88 41966.73 59830.52
Jul 21       50898.63 44878.94 56918.31 41692.32 60104.94
Aug 21       50898.63 44704.71 57092.55 41425.84 60371.41
Sep 21       50898.63 44535.24 57262.02 41166.66 60630.59
Oct 21       50898.63 44370.17 57427.09 40914.21 60883.05
Nov 21       50898.63 44209.17 57588.09 40667.98 61129.27
Dec 21       50898.63 44051.96 57745.30 40427.55 61369.71
Jan 22       50898.63 43898.27 57898.99 40192.51 61604.75
Feb 22       50898.63 43747.89 58049.37 39962.52 61834.74
Mar 22       50898.63 43600.61 58196.65 39737.27 62059.99
plot(fore_fit)

astsa::sarima.for(z, 25, 0,1,1)
$pred
A Time Series: 3 × 12
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
20 50890.61 50882.70 50874.80 50866.90 50858.99 50851.09 50843.18 50835.28 50827.38 50819.47
21 50811.57 50803.67 50795.76 50787.86 50779.95 50772.05 50764.15 50756.24 50748.34 50740.43 50732.53 50724.63
22 50716.72 50708.82 50700.92
$se
A Time Series: 3 × 12
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
20 1154.070 1620.915 1980.620 2284.369 2552.221 2794.516 3017.417 3224.949 3419.910 3604.341
21 3779.783 3947.436 4108.252 4263.006 4412.336 4556.775 4696.774 4832.719 4964.943 5093.737 5219.352 5342.015
22 5461.924 5579.257 5694.172 

astsa::sarima.for(lag_z, 25, 0,0,1)
$pred
A Time Series: 3 × 12
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
20 -9.392518 -7.903833 -7.903833 -7.903833 -7.903833 -7.903833 -7.903833 -7.903833 -7.903833 -7.903833
21 -7.903833 -7.903833 -7.903833 -7.903833 -7.903833 -7.903833 -7.903833 -7.903833 -7.903833 -7.903833 -7.903833 -7.903833
22 -7.903833 -7.903833 -7.903833
$se
A Time Series: 3 × 12
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
20 1154.07 1154.18 1154.18 1154.18 1154.18 1154.18 1154.18 1154.18 1154.18 1154.18
21 1154.18 1154.18 1154.18 1154.18 1154.18 1154.18 1154.18 1154.18 1154.18 1154.18 1154.18 1154.18
22 1154.18 1154.18 1154.18

8:2

train_data <- window(z, start = start(z), end = index(z)[184])
test_data <- window(z, start = index(z)[185])
length(train_data)
184 
length(test_data)
46 
test_data
A Time Series: 5 × 12
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
16 43950 41600 40850 42050 41400 42650 43650 43200
17 43150 42800 41800 40500 39050 37950 39600 38950 37650 37750 38000 37800
18 37600 38550 41300 44700 43750 43950 45600 45650 45000 46350 48300 48200
19 47500 47800 49250 50300 50300 50500 49850 51100 50500 50500 49700 50800
20 50800 50900 
astsa::sarima.for(train_data, 46, 0,1,1)
$pred
A Time Series: 5 × 12
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
16 43765.61 43716.78 43667.94 43619.11 43570.28 43521.44 43472.61 43423.78
17 43374.95 43326.11 43277.28 43228.45 43179.61 43130.78 43081.95 43033.11 42984.28 42935.45 42886.61 42837.78
18 42788.95 42740.11 42691.28 42642.45 42593.61 42544.78 42495.95 42447.12 42398.28 42349.45 42300.62 42251.78
19 42202.95 42154.12 42105.28 42056.45 42007.62 41958.78 41909.95 41861.12 41812.28 41763.45 41714.62 41665.79
20 41616.95 41568.12
$se
A Time Series: 5 × 12
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
16 1154.524 1581.835 1916.110 2200.172 2451.537 2679.423 2889.392 3085.103
17 3269.119 3443.314 3609.112 3767.621 3919.725 4066.143 4207.469 4344.200 4476.756 4605.499 4730.740 4852.749
18 4971.765 5087.998 5201.635 5312.841 5421.767 5528.547 5633.304 5736.147 5837.179 5936.492 6034.171 6130.293
19 6224.931 6318.152 6410.017 6500.584 6589.907 6678.035 6765.015 6850.891 6935.703 7019.491 7102.291 7184.136
20 7265.059 7345.091 

arima_model <- arima(train_data, order = c(0, 1, 1))

# 훈련 세트 예측
train_pred <- predict(arima_model, n.ahead = length(train_data))

# 테스트 세트 예측
test_pred <- predict(arima_model, n.ahead = length(test_data))

# 시각화
plot(train_data, col = "blue", type = "l", lty = 1, lwd = 2, main = "ARIMA Model Forecast")
lines(train_pred$pred, col = "red", lty = 2, lwd = 2)
lines(test_pred$pred, col = "green", lty = 2, lwd = 2)
legend("topright", legend = c("Original", "Train Prediction", "Test Prediction"), col = c("blue", "red", "green"), lty = c(1, 2, 2), lwd = c(2, 2, 2))

# ARIMA 모델 적합
arima_model <- arima(train_data, order = c(0, 1, 1))

# 훈련 세트 예측
train_pred <- predict(arima_model, n.ahead = length(train_data))$pred + diff(train_data)[1]

# 테스트 세트 예측
test_pred <- predict(arima_model, n.ahead = length(test_data))$pred + diff(train_data)[length(train_data)]

# 시각화
plot(data, col = "blue", type = "l", lty = 1, lwd = 2, main = "ARIMA Model Forecast")
lines(train_pred, col = "red", lty = 2, lwd = 2)
lines(c(rep(NA, length(train_data)), test_pred), col = "green", lty = 2, lwd = 2)
legend("topright", legend = c("Original", "Train Prediction", "Test Prediction"), col = c("blue", "red", "green"), lty = c(1, 2, 2), lwd = c(2, 2, 2))

  • index가 안맞아서 위와같이 되네;; 흠..
data <- kakao$종가
length(data)
230 
tr <- data[1:184]
ts <- data[185:length(data)]
astsa::sarima.for(tr, 46, 0,1,1)
$pred
A Time Series:
  1. 43765.6102424124
  2. 43716.777101872
  3. 43667.9439613316
  4. 43619.1108207913
  5. 43570.2776802509
  6. 43521.4445397106
  7. 43472.6113991702
  8. 43423.7782586298
  9. 43374.9451180894
  10. 43326.1119775491
  11. 43277.2788370087
  12. 43228.4456964683
  13. 43179.612555928
  14. 43130.7794153876
  15. 43081.9462748472
  16. 43033.1131343069
  17. 42984.2799937665
  18. 42935.4468532261
  19. 42886.6137126858
  20. 42837.7805721454
  21. 42788.947431605
  22. 42740.1142910647
  23. 42691.2811505243
  24. 42642.4480099839
  25. 42593.6148694436
  26. 42544.7817289032
  27. 42495.9485883628
  28. 42447.1154478225
  29. 42398.2823072821
  30. 42349.4491667417
  31. 42300.6160262014
  32. 42251.782885661
  33. 42202.9497451206
  34. 42154.1166045803
  35. 42105.2834640399
  36. 42056.4503234995
  37. 42007.6171829592
  38. 41958.7840424188
  39. 41909.9509018784
  40. 41861.1177613381
  41. 41812.2846207977
  42. 41763.4514802573
  43. 41714.618339717
  44. 41665.7851991766
  45. 41616.9520586362
  46. 41568.1189180958
$se
A Time Series:
  1. 1154.52422170161
  2. 1581.83516172709
  3. 1916.11032543969
  4. 2200.17160231584
  5. 2451.53653450596
  6. 2679.4230125902
  7. 2889.39162814223
  8. 3085.10296119252
  9. 3269.11862457442
  10. 3443.31422933193
  11. 3609.11196588582
  12. 3767.62066597484
  13. 3919.72470756061
  14. 4066.1429000272
  15. 4207.46888090952
  16. 4344.19965979955
  17. 4476.75630167457
  18. 4605.49924383485
  19. 4730.73985602082
  20. 4852.74931206263
  21. 4971.76549991095
  22. 5087.99847547984
  23. 5201.6348186763
  24. 5312.84115019884
  25. 5421.76699864782
  26. 5528.54715888424
  27. 5633.30364780627
  28. 5736.14733848146
  29. 5837.1793350169
  30. 5936.49213673604
  31. 6034.17062983052
  32. 6130.2929367437
  33. 6224.93114746422
  34. 6318.15195219699
  35. 6410.01719119622
  36. 6500.58433464343
  37. 6589.90690315061
  38. 6678.03483762794
  39. 6765.0148257748
  40. 6850.89059125406
  41. 6935.70315063396
  42. 7019.49104238294
  43. 7102.29053154507
  44. 7184.13579318036
  45. 7265.05907720203
  46. 7345.09085686597