Phân tích mã GAS bằng model ARIMA
Pham Dinh Khanh
April 22, 2017
I. Dữ liệu
Dữ liệu thu thập là giá đóng cửa có điều chỉnh của mã chứng khoán GAS trong khoảng thời gian từ ngày 16/09/2016 đến 21/04/2017 được thu thập từ trang chủ của Vndirect:
Chia tập dữ liệu thành 2 phần là train và test theo tỷ lệ 9:1. Trong đó tập train sẽ chiếm 90% số quan sát ngày đầu tiên và test chiếm 10% số quan sát những ngày cuối cùng. Tập train được sử dụng để hồi qui model và tập test được dùng để kiểm định tính chính xác của model.
## 'data.frame': 150 obs. of 7 variables:
## $ DATE : Factor w/ 325 levels "01/02/2016","01/03/2016",..: 256 221 209 197 187 177 142 130 118 109 ...
## $ CLOSE : num 54.1 53.6 54 55 55.1 54 53.9 54.7 55.4 56.8 ...
## $ TICKER: Factor w/ 1 level "GAS": 1 1 1 1 1 1 1 1 1 1 ...
## $ OPEN : num 53.6 53.9 54.4 55.2 54 54.2 54.9 56.4 57 57 ...
## $ HIGH : num 54.5 54.4 54.4 55.4 55.2 55.1 55 56.4 57 57.5 ...
## $ LOW : num 53.4 53.6 54 54.7 54 53.7 53.5 54.3 55.4 56.3 ...
## $ VOLUME: num 361260 256750 405730 247430 457560 ...## PRICE
## 2016-09-16 63.2
## 2016-09-19 64.0
## 2016-09-20 66.0
## 2016-09-21 67.6
## 2016-09-22 67.8
## 2016-09-23 68.6## [1] "6 quan sat dau tien test data"## PRICE
## 2017-04-17 54.0
## 2017-04-18 55.1
## 2017-04-19 55.0
## 2017-04-20 54.0
## 2017-04-21 53.6
## 2017-04-24 54.1## [1] "Kich thuoc mau test data"## [1] 15## [1] "6 quan sat dau tien cua train data"## PRICE
## 2017-03-24 54.5
## 2017-03-27 54.0
## 2017-03-28 53.6
## 2017-03-29 53.8
## 2017-03-30 54.4
## 2017-03-31 55.0## [1] "Kich thuoc mau train data"## [1] 135## [1] "Chuoi loi suat thuc te theo ngay"## PRICE
## 2017-04-17 0.001853569
## 2017-04-18 0.020165670
## 2017-04-19 -0.001816531
## 2017-04-20 -0.018349139
## 2017-04-21 -0.007434978
## 2017-04-24 0.009285118
##
## Augmented Dickey-Fuller Test
##
## data: data.xts
## Dickey-Fuller = -5.3932, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary
## [1] 135## PRICE
## 2017-03-31 0.01096903##
## Forecast method: ARIMA(1,0,2) with zero mean
##
## Model Information:
##
## Call:
## arima(x = stock_train, order = c(1, 0, 2), include.mean = FALSE)
##
## Coefficients:
## ar1 ma1 ma2
## 0.8481 -0.9424 0.0738
## s.e. NaN NaN NaN
##
## sigma^2 estimated as 0.0002981: log likelihood = 353.78, aic = -699.55
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.001212412 0.01726464 0.01229523 NaN Inf 0.6681695
## ACF1
## Training set -0.004937111
##
## Forecasts:
## Point Forecast Lo 75 Hi 75
## 135 -0.001085834 -0.02094621 0.01877454
##
## Forecast method: ARIMA(1,0,2) with zero mean
##
## Model Information:
##
## Call:
## arima(x = stock_train, order = c(1, 0, 2), include.mean = FALSE)
##
## Coefficients:
## ar1 ma1 ma2
## 0.5508 -0.6466 0.0288
## s.e. 0.8995 0.9030 0.1444
##
## sigma^2 estimated as 0.0002958: log likelihood = 356.94, aic = -705.88
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.001262739 0.01719789 0.01227886 NaN Inf 0.6678114
## ACF1
## Training set -0.005516154
##
## Forecasts:
## Point Forecast Lo 75 Hi 75
## 136 -3.658368e-05 -0.01982017 0.019747
##
## Forecast method: ARIMA(1,0,2) with zero mean
##
## Model Information:
##
## Call:
## arima(x = stock_train, order = c(1, 0, 2), include.mean = FALSE)
##
## Coefficients:
## ar1 ma1 ma2
## 0.5397 -0.6349 0.0247
## s.e. 0.8474 0.8505 0.1390
##
## sigma^2 estimated as 0.000294: log likelihood = 359.99, aic = -711.99
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.001313255 0.01714582 0.01224962 NaN Inf 0.6706839
## ACF1
## Training set -0.005878081
##
## Forecasts:
## Point Forecast Lo 75 Hi 75
## 137 0.0005437096 -0.01917997 0.02026739
##
## Forecast method: ARIMA(1,0,2) with zero mean
##
## Model Information:
##
## Call:
## arima(x = stock_train, order = c(1, 0, 2), include.mean = FALSE)
##
## Coefficients:
## ar1 ma1 ma2
## 0.5214 -0.6181 0.0243
## s.e. 0.9140 0.9174 0.1443
##
## sigma^2 estimated as 0.0002924: log likelihood = 363.02, aic = -718.03
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.00123776 0.01709888 0.01221873 NaN Inf 0.6694666
## ACF1
## Training set -0.005750467
##
## Forecasts:
## Point Forecast Lo 75 Hi 75
## 138 -0.0007114348 -0.02038112 0.01895825
##
## Forecast method: ARIMA(1,0,2) with zero mean
##
## Model Information:
##
## Call:
## arima(x = stock_train, order = c(1, 0, 2), include.mean = FALSE)
##
## Coefficients:
## ar1 ma1 ma2
## 0.8501 -0.9379 0.0660
## s.e. NaN NaN 0.0733
##
## sigma^2 estimated as 0.0003043: log likelihood = 362.91, aic = -717.82
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.0009030651 0.01744384 0.01241228 NaN Inf 0.675896
## ACF1
## Training set -0.002380377
##
## Forecasts:
## Point Forecast Lo 75 Hi 75
## 139 -0.003844981 -0.02391149 0.01622153
##
## Forecast method: ARIMA(1,0,2) with zero mean
##
## Model Information:
##
## Call:
## arima(x = stock_train, order = c(1, 0, 2), include.mean = FALSE)
##
## Coefficients:
## ar1 ma1 ma2
## 0.85 -0.9393 0.0674
## s.e. NaN NaN 0.0689
##
## sigma^2 estimated as 0.0003021: log likelihood = 366.04, aic = -724.08
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.0009078543 0.01738136 0.01233241 NaN Inf 0.6637528
## ACF1
## Training set -0.001409079
##
## Forecasts:
## Point Forecast Lo 75 Hi 75
## 140 -0.0002707824 -0.02026542 0.01972385
##
## Forecast method: ARIMA(1,0,2) with zero mean
##
## Model Information:
##
## Call:
## arima(x = stock_train, order = c(1, 0, 2), include.mean = FALSE)
##
## Coefficients:
## ar1 ma1 ma2
## 0.8496 -0.939 0.0669
## s.e. NaN NaN 0.0678
##
## sigma^2 estimated as 3e-04: log likelihood = 369.17, aic = -730.34
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.0009162767 0.01731961 0.01225645 NaN Inf 0.6635388
## ACF1
## Training set -0.001384932
##
## Forecasts:
## Point Forecast Lo 75 Hi 75
## 141 -0.0002065136 -0.02013011 0.01971709
##
## Forecast method: ARIMA(1,0,2) with zero mean
##
## Model Information:
##
## Call:
## arima(x = stock_train, order = c(1, 0, 2), include.mean = FALSE)
##
## Coefficients:
## ar1 ma1 ma2
## 0.4996 -0.5888 0.0041
## s.e. 0.7122 0.7133 0.1226
##
## sigma^2 estimated as 0.0003017: log likelihood = 371.41, aic = -734.82
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.001101812 0.01736854 0.01239993 NaN Inf 0.6700822
## ACF1
## Training set -0.003034996
##
## Forecasts:
## Point Forecast Lo 75 Hi 75
## 142 0.001696384 -0.01828351 0.02167628
##
## Forecast method: ARIMA(1,0,2) with zero mean
##
## Model Information:
##
## Call:
## arima(x = stock_train, order = c(1, 0, 2), include.mean = FALSE)
##
## Coefficients:
## ar1 ma1 ma2
## 0.5340 -0.6153 0.0005
## s.e. 0.6508 0.6522 0.1150
##
## sigma^2 estimated as 0.000301: log likelihood = 374.2, aic = -740.41
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.001200022 0.01734874 0.01242842 NaN Inf 0.6732381
## ACF1
## Training set -0.003979315
##
## Forecasts:
## Point Forecast Lo 75 Hi 75
## 143 0.00188112 -0.01807599 0.02183823
##
## Forecast method: ARIMA(1,0,2) with zero mean
##
## Model Information:
##
## Call:
## arima(x = stock_train, order = c(1, 0, 2), include.mean = FALSE)
##
## Coefficients:
## ar1 ma1 ma2
## 0.5621 -0.6373 0.0035
## s.e. 0.6721 0.6740 0.1091
##
## sigma^2 estimated as 0.0003008: log likelihood = 376.89, aic = -745.78
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.001294965 0.01734312 0.01245064 NaN Inf 0.6786989
## ACF1
## Training set -0.005211916
##
## Forecasts:
## Point Forecast Lo 75 Hi 75
## 144 0.002130153 -0.01782049 0.0220808
##
## Forecast method: ARIMA(1,0,2) with zero mean
##
## Model Information:
##
## Call:
## arima(x = stock_train, order = c(1, 0, 2), include.mean = FALSE)
##
## Coefficients:
## ar1 ma1 ma2
## 0.5692 -0.6443 0.0043
## s.e. 0.6645 0.6668 0.1091
##
## sigma^2 estimated as 0.0002987: log likelihood = 380.03, aic = -752.05
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.001288557 0.01728277 0.01236611 NaN Inf 0.6745429
## ACF1
## Training set -0.005613988
##
## Forecasts:
## Point Forecast Lo 75 Hi 75
## 145 0.001153111 -0.01872811 0.02103433
##
## Forecast method: ARIMA(1,0,2) with zero mean
##
## Model Information:
##
## Call:
## arima(x = stock_train, order = c(1, 0, 2), include.mean = FALSE)
##
## Coefficients:
## ar1 ma1 ma2
## 0.5617 -0.6376 -0.0042
## s.e. 0.5548 0.5567 0.1055
##
## sigma^2 estimated as 0.0002991: log likelihood = 382.57, aic = -757.13
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.001175771 0.01729415 0.01243551 NaN Inf 0.6783339
## ACF1
## Training set -0.004775439
##
## Forecasts:
## Point Forecast Lo 75 Hi 75
## 146 -0.0006327303 -0.02052704 0.01926158
##
## Forecast method: ARIMA(1,0,2) with zero mean
##
## Model Information:
##
## Call:
## arima(x = stock_train, order = c(1, 0, 2), include.mean = FALSE)
##
## Coefficients:
## ar1 ma1 ma2
## 0.5614 -0.6379 -0.0036
## s.e. 0.5532 0.5554 0.1052
##
## sigma^2 estimated as 0.000297: log likelihood = 385.7, aic = -763.41
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.001175675 0.0172351 0.01235746 NaN Inf 0.6731522
## ACF1
## Training set -0.004116331
##
## Forecasts:
## Point Forecast Lo 75 Hi 75
## 147 -0.0003423334 -0.02016871 0.01948405
##
## Forecast method: ARIMA(1,0,2) with zero mean
##
## Model Information:
##
## Call:
## arima(x = stock_train, order = c(1, 0, 2), include.mean = FALSE)
##
## Coefficients:
## ar1 ma1 ma2
## 0.5272 -0.6037 -0.0096
## s.e. 0.5792 0.5811 0.1077
##
## sigma^2 estimated as 0.0002972: log likelihood = 388.3, aic = -768.61
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.001289639 0.01724008 0.01239958 NaN Inf 0.6759069
## ACF1
## Training set -0.004333645
##
## Forecasts:
## Point Forecast Lo 75 Hi 75
## 148 0.001155483 -0.01867664 0.0209876
##
## Forecast method: ARIMA(1,0,2) with zero mean
##
## Model Information:
##
## Call:
## arima(x = stock_train, order = c(1, 0, 2), include.mean = FALSE)
##
## Coefficients:
## ar1 ma1 ma2
## 0.5243 -0.5974 -0.0123
## s.e. 0.5709 0.5721 0.1052
##
## sigma^2 estimated as 0.0002957: log likelihood = 391.32, aic = -774.65
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.001334693 0.01719615 0.01237496 NaN Inf 0.6764288
## ACF1
## Training set -0.005046805
##
## Forecasts:
## Point Forecast Lo 75 Hi 75
## 149 0.00141473 -0.01836685 0.02119631
## Actual_series FORECAST Accuracy
## 2017-04-03 -0.005469476 -1.085834e-03 1
## 2017-04-04 -0.007339482 -3.658368e-05 1
## 2017-04-05 0.009165967 5.437096e-04 1
## 2017-04-07 0.042863704 -7.114348e-04 0
## 2017-04-10 -0.005258557 -3.844981e-03 1
## 2017-04-11 -0.001759015 -2.707824e-04 1
## 2017-04-12 -0.024956732 -2.065136e-04 1
## 2017-04-13 -0.012715884 1.696384e-03 0
## 2017-04-14 -0.014733232 1.881120e-03 0
## 2017-04-17 0.001853569 2.130153e-03 1
## 2017-04-18 0.020165670 1.153111e-03 1
## 2017-04-19 -0.001816531 -6.327303e-04 1
## 2017-04-20 -0.018349139 -3.423334e-04 1
## 2017-04-21 -0.007434978 1.155483e-03 0
## 2017-04-24 0.009285118 1.414730e-03 1## [1] 73.33333Như vậy model dự báo chính xác được 73.3% số trường hợp tăng, giảm của mã GAS.
Dự báo diễn biến giá đóng cửa ngày mai: 54.2 tăng nhẹ so với hôm trước.
Khoảng tin cậy 95% của giá đóng cửa [52.4,56.0].
Khoảng tin cậy 90% của giá đóng cửa [52.7, 55.7].
Khoảng tin cậy 75% của giá đóng cửa [55.1,55.3].