R的多個季節性的arima模型

Question

我正在學習創建具有多個季節性的時間序列的預測模型。以下是我所指的數據集的子集。此數據集包括小時數據點，我希望在我的arima模型中包含每日和每週季節性。以下是數據集的子集：

data= c(4,4,1,2,6,21,105,257,291,172,72,10,35,42,77,72,133,192,122,59,29,25,24,5,7,3,3,0,7,15,91,230,284,147,67,53,54,55,63,73,114,154,137,57,27,31,25,11,4,4,4,2,7,18,68,218,251,131,71,43,55,62,63,80,120,144,107,42,27,11,10,16,8,10,7,1,4,3,12,17,58,59,68,76,91,95,89,115,107,107,41,40,25,18,14,15,6,12,2,4,1,6,9,14,43,67,67,94,100,129,126,122,132,118,68,26,19,12,9,5,4,2,5,1,3,16,89,233,304,174,53,55,53,52,59,92,117,214,139,73,37,28,15,11,8,1,2,5,4,22,103,258,317,163,58,29,37,46,54,62,95,197,152,58,32,30,17,9,8,1,3,1,3,16,109,245,302,156,53,34,47,46,54,65,102,155,116,51,30,24,17,10,7,4,8,0,11,0,2,225,282,141,4,87,44,60,52,74,135,157,113,57,44,26,29,17,8,7,4,4,2,10,57,125,182,100,33,27,41,39,35,50,69,92,66,30,11,10,11,9,6,5,10,4,1,7,9,17,24,21,29,28,48,38,30,21,26,25,35,10,9,4,4,4,3,5,4,4,4,3,5,10,16,28,47,63,40,49,28,22,18,27,18,10,5,8,7,3,2,2,4,1,4,19,59,167,235,130,57,45,46,42,40,49,64,96,54,27,17,18,15,7,6,2,3,1,2,21,88,187,253,130,77,47,49,48,53,77,109,147,109,45,41,35,16,13) 

我試圖使用的代碼如下：

tsdata = ts (data, frequency = 24) 

aicvalstemp = NULL 
aicvals= NULL 

for (i in 1:5) { 
    for (j in 1:5) { 
    xreg1 = fourier(tsdata,i,24) 
    xreg2 = fourier(tsdata,j,168) 
    xregs = cbind(xreg1,xreg2) 
    armodel = auto.arima(bike_TS_west, xreg = xregs) 
    aicvalstemp = cbind(i,j,armodel$aic) 
    aicvals = rbind(aicvals,aicvalstemp) 
    } 

} 

因爲xreg1和xreg2行數是在上面的命令的cbind命令失敗不同。我甚至嘗試在傅立葉函數中使用1：length（data）參數，但這也給我一個錯誤。如果有人能夠糾正上述代碼中的錯誤，以使用AIC值最小的arima模型預測未來24小時，這將非常有幫助。另外，如果您可以通過創建培訓和測試數據集在代碼中包含數據分割，那將非常棒。謝謝你的幫助。

Answer 1

我不明白爲這些數據填入每週「季節」的願望，因爲您提供的數據子集中沒有證據。另外，您應該對數據進行對數轉換，因爲它們並不像原樣反映高斯過程。

因此，您可以通過某種形式的小時信號來擬合模型。

## the data are not normal, so log transform to meet assumption of Gaussian errors 
ln_dat <- log(tsdata) 
## number of hours to forecast 
hrs_out <- 24 
## max number of Fourier terms 
max_F <- 5 
## empty list for model fits 
mod_res <- vector("list", max_F) 
## fit models with increasing Fourier terms 
for (i in 1:max_F) { 
    xreg <- fourier(ln_dat,i) 
    mod_res[[i]] <- auto.arima(tsdata, xreg = xreg) 
} 
## table of AIC results 
aic_tbl <- data.frame(F=seq(max_F), AIC=sapply(mod_res, AIC)) 
## number of Fourier terms in best model 
F_best <- which(aic_tbl$AIC==min(aic_tbl$AIC)) 
## forecast from best model 
fore <- forecast(mod_res[[F_best]], xreg=fourierf(ln_dat,F_best,hrs_out))