ARIMAX预测（auto.arima）的问题

Question

我正在尝试使用带有外生回归变量的auto.arima函数来预测每月的累积时间序列（请参见下面的数据）。我有两个问题。

1）我的第一个问题是，当我拟合模型并使用预测函数预测2019年下半年时，从此预测图中可以看到，预测从零开始。

仅当我包括一个外源回归矩阵时，才会发生这种情况，而当我使用单个时间序列作为回归图时，则不会发生这种情况。

那是为什么？我的代码是：

regnskab <- ts(data$Regnskab, frequency = 12, start = c(2014,1), end = c(2019,6))
budget <- ts(data$Budget, frequency = 12, start = c(2014,1), end = c(2019,6))
dagtilbud <- ts(data$Dagtilbud, frequency = 12, start = c(2014,1), end = c(2019,6))
skole <- ts(data$Skole, frequency = 12, start = c(2014,1), end = c(2019,6))
sundhed <- ts(data$Sundhed, frequency = 12, start = c(2014,1), end = c(2019,6))
miljø <- ts(data$Miljø, frequency = 12, start = c(2014,1), end = c(2019,6))

tsmatrix <- cbind(budget, dagtilbud, miljø, skole, sundhed)

fit <- auto.arima(regnskab, xreg = tsmatrix)
fcast <- forecast(fit, h = 6, xreg = tsmatrix)
autoplot(fcast)
summary(fcast)

2）我的第二个问题是我希望对未来6个月进行预测，但是在包括外生回归变量时，h = 6选项不适用。可以通过任何方式解决吗？同样，没有外源回归变量也不是问题。

希望您能为垃圾邮件发送问题提供帮助和抱歉！

我的模型摘要：

> summary(fcast)

Forecast method: Regression with ARIMA(1,0,0)(1,0,0)[12] errors

Model Information:
Series: regnskab 
Regression with ARIMA(1,0,0)(1,0,0)[12] errors 

Coefficients:
         ar1    sar1  budget  dagtilbud   miljø   skole  sundhed
      0.7466  0.6693  0.0101     2.0861  0.1037  2.5240   7.7623
s.e.  0.0935  0.1042  0.0077     0.6967  1.7672  0.7535   2.6611

sigma^2 estimated as 1.884:  log likelihood=-114.84
AIC=245.68   AICc=248.21   BIC=263.2

Error measures:
                      ME     RMSE       MAE        MPE      MAPE      MASE        ACF1
Training set -0.01739231 1.297694 0.9002519 -0.1065542 0.9060671 0.3687968 -0.03222251

> regnskab
           Jan       Feb       Mar       Apr       May       Jun       Jul       Aug       Sep       Oct       Nov       Dec
2014  19.11281  36.68003  54.66383  74.93864  94.10328 113.36373 134.96638 152.75095 170.79800 189.55430 207.00803 227.82096
2015  18.90205  37.20079  55.73305  75.44689  94.74538 115.03997 136.79829 155.41164 173.69889 191.96484 210.42391 231.52982
2016  20.12939  38.51516  56.32522  78.04822  97.46681 116.58424 139.43255 157.83048 175.26727 195.06259 213.73833 234.45281
2017  20.43082  38.55219  57.50119  78.07558  97.50132 119.13735 141.71973 161.49281 180.32002 199.27769 216.92571 239.40683
2018  19.35194  37.40571  55.36897  76.33412  95.90922 117.41442 140.03545 159.10527 177.88068 194.43207 215.28905 245.85670
2019  20.85722  40.01691  59.97383  81.92719 103.15225 123.81454

> tsmatrix
           budget dagtilbud    miljø     skole  sundhed
Jan 2014 230.0605  2.616639 0.597125  3.193017 0.456470
Feb 2014 230.0605  5.025708 1.047983  6.402845 1.012468
Mar 2014 230.0605  7.548424 1.458105  9.816814 1.602384
Apr 2014 230.0605 10.350321 1.957022 13.446215 2.263646
May 2014 230.0605 12.913356 2.439587 17.100957 2.873934
Jun 2014 230.0605 15.380146 2.915020 20.791343 3.498350
Jul 2014 230.0605 17.931069 3.434464 23.701276 3.987042
Aug 2014 230.0605 20.441732 3.837721 27.319389 4.597127
Sep 2014 230.0605 22.839922 4.295486 30.859254 5.185271
Oct 2014 230.0605 25.234620 4.761740 34.350629 5.819948
Nov 2014 230.0605 27.554525 5.163576 37.688182 6.416112
Dec 2014 230.0605 30.109529 5.742699 42.095747 7.313195
Jan 2015 234.5089  2.404843 0.643976  3.185265 0.477921
Feb 2015 234.5089  5.090533 1.094641  6.654691 1.040235
Mar 2015 234.5089  7.319261 1.462134 10.168618 1.659232
Apr 2015 234.5089 10.040823 1.943120 14.082780 2.356247
May 2015 234.5089 12.470742 2.431818 17.827494 2.963360
Jun 2015 234.5089 14.846720 3.019969 21.612527 3.615607
Jul 2015 234.5089 17.543682 3.540084 24.702634 4.126374
Aug 2015 234.5089 19.786612 3.984587 28.330977 4.741392
Sep 2015 234.5089 22.037785 4.362497 31.942762 5.367815
Oct 2015 234.5089 24.347196 4.805391 35.423452 6.019133
Nov 2015 234.5089 26.751255 5.250481 38.964450 6.642436
Dec 2015 234.5089 29.276667 5.789919 43.428855 7.555361
Jan 2016 237.2361  2.538133 0.721184  3.352676 0.508847
Feb 2016 237.2361  4.906975 1.377086  6.804320 1.100914
Mar 2016 237.2361  7.184724 1.719629 10.290800 1.744743
Apr 2016 237.2361  9.895237 2.333842 14.223635 2.480869
May 2016 237.2361 12.316509 2.850905 17.957433 3.115473
Jun 2016 237.2361 14.578536 3.404785 21.759111 3.858713
Jul 2016 237.2361 17.215216 3.867858 24.949928 4.359129
Aug 2016 237.2361 19.399769 4.406750 28.503968 5.030926
Sep 2016 237.2361 21.702215 4.792190 32.112449 5.674259
Oct 2016 237.2361 24.112579 5.238401 35.625806 6.328084
Nov 2016 237.2361 26.453919 5.677270 39.158270 6.977991
Dec 2016 237.2361 28.969565 6.098136 43.558768 7.974787
Jan 2017 241.9089  2.538901 0.917354  3.488151 0.535639
Feb 2017 241.9089  4.847981 1.450172  6.857674 1.138782
Mar 2017 241.9089  7.281994 1.899543 10.394615 1.808938
Apr 2017 241.9089 10.031959 2.388542 14.335895 2.554613
May 2017 241.9089 12.411935 2.893036 18.042788 3.206503
Jun 2017 241.9089 14.982942 3.282057 22.137085 3.959622
Jul 2017 241.9089 17.567382 3.770244 25.392706 4.540047
Aug 2017 241.9089 19.738993 4.484434 29.108498 5.196528
Sep 2017 241.9089 22.273634 5.051894 32.693173 5.870257
Oct 2017 241.9089 24.636583 5.456458 36.203329 6.544383
Nov 2017 241.9089 27.259158 5.793056 39.867875 7.249982
Dec 2017 241.9089 29.831986 6.079033 44.273697 8.269454
Jan 2018 246.0944  2.467981 0.985846  3.377469 0.544258
Feb 2018 246.0944  4.877189 1.383190  6.815726 1.167431
Mar 2018 246.0944  7.367918 1.738033 10.486250 1.848972
Apr 2018 246.0944 10.148353 2.249466 14.439246 2.614913
May 2018 246.0944 12.687311 2.844656 18.194669 3.328234
Jun 2018 246.0944 15.482606 3.616200 22.433048 4.108966
Jul 2018 246.0944 17.715938 3.982451 25.305411 4.689087
Aug 2018 246.0944 20.077201 4.696088 29.018017 5.396796
Sep 2018 246.0944 22.659831 5.158706 32.860215 6.087975
Oct 2018 246.0944 24.719623 5.586616 36.143198 6.713136
Nov 2018 246.0944 27.750904 6.069519 40.237747 7.501346
Dec 2018 246.0944 30.326036 6.308786 44.733470 8.564162
Jan 2019 251.9230  2.653607 0.932776  3.501389 0.595458
Feb 2019 251.9230  5.070721 1.445741  6.991538 1.243721
Mar 2019 251.9230  7.542256 1.825956 10.737607 1.941444
Apr 2019 251.9230 10.301781 2.330015 14.647082 2.733956
May 2019 251.9230 13.193286 2.999816 18.671285 3.455616
Jun 2019 251.9230 15.423716 3.516735 22.612031 4.145206

Answer 1

预测函数中的xreg矩阵应用于将来的时间段。如果您希望h = 6，则给出一个与6个周期相对应的6行矩阵。