ARIMAX 中的标准误差得到 NaN 结果

Question

我想应用关于灾难对夜光强度影响的中断时间序列分析。我有从 2015 年 1 月到 2020 年 5 月的 65 个月的数据。灾难发生在 2018 年 10 月（原始数据的 46 个月）。对于干预前的数据，我有一个 arima 模型函数 ARIMA(3,0,0),(0,0,0)12

干预函数是这样的

the transfer function

enter image description here

所以我这里有代码

air.m1=arimax(kota,order=c(3,0,0),
          seasonal=list(order=c(0,0,0),period=12),
          xtransf=data.frame(I911=1*(seq(kota)==46),
                             I911=1*(seq(kota)==46)),transfer=list(c(0,0),c(1,0)))

当我试图知道结果时，我收到了这样的警告

    Coefficients:
              ar1      ar2  I911-MA0  I911.1-AR1  I911.1-MA0
          -0.8738  -0.5048  800.1583      0.0526   -2283.138
    s.e.   0.1118   0.1114       NaN         NaN         NaN
    
    sigma^2 estimated as 1826510:  log likelihood = -552.69,  aic = 1115.37
Warning message:
In sqrt(diag(x$var.coef)) : NaNs produced

为什么没有出现标准错误？这个问题的解决方案是什么？

这是 kota 变量的样子

          Jan      Feb      Mar      Apr      May      Jun      Jul      Aug
2015 3627.300 3982.730 3763.880 4568.350 4463.370 3492.180 4689.460 4134.270
2016 3495.830  304.790 4093.980 3696.690 3339.750 2053.980 4105.550 4417.260
2017 3279.070 3064.600 6164.940 2507.610 2835.330 4245.300  421.230 4252.740
2018  161.870 4919.110 3952.470 5848.790 4862.430 4787.780 4905.020 6036.310
2019 3610.630 4413.600 3123.320 5432.030 5050.170 3127.430 6437.540 5001.340
2020 5283.910 5047.740 4971.200 7375.960 3862.400                           
          Sep      Oct      Nov      Dec
2015 3671.630 3392.750 2407.510 3374.650
2016 4354.850 5184.930 1731.430 4675.500
2017 4864.100 2747.270 3795.644 4697.800
2018 5431.930 3224.620 1880.110 3955.170
2019 5577.980 6907.160 5669.520 6981.180
2020

Answer 1

按照交叉验证上关于此 post 的指导，您的数据似乎显示出显着的异方差性。通过用 log():

包装 kota 来尝试对数据进行对数转换

library(TSA)
library(lmtest)
# data
vec <- c(3627.300, 3982.730, 3763.880, 4568.350, 4463.370, 3492.180, 4689.460, 
  4134.270, 3671.630, 3392.750, 2407.510, 3374.650, 3495.830,  304.790,
  4093.980, 3696.690, 3339.750, 2053.980, 4105.550, 4417.260, 4354.850, 
  5184.930, 1731.430, 4675.500, 3279.070, 3064.600, 6164.940, 2507.610,
  2835.330, 4245.300,  421.230, 4252.740, 4864.100, 2747.270, 3795.644, 
  4697.800, 161.870, 4919.110, 3952.470, 5848.790, 4862.430, 4787.780, 
  4905.020, 6036.310, 5431.930, 3224.620, 1880.110, 3955.170, 3610.630,
  4413.600, 3123.320, 5432.030, 5050.170, 3127.430, 6437.540, 5001.340,
  5577.980, 6907.160, 5669.520, 6981.180, 5283.910, 5047.740, 4971.200, 
  7375.960, 3862.400)                           

# convert to time series
kota <- ts(vec, start=c(2015, 1), end=c(2020, 1), frequency=12)

# test heteroscedasticity
> gqtest(kota ~ 1)

    Goldfeld-Quandt test

data:  kota ~ 1
GQ = 2.0991, df1 = 30, df2 = 29, p-value = 0.02451
alternative hypothesis: variance increases from segment 1 to 2

# log tranform time series object
air.m1=arimax(log(kota),order=c(3,0,0), # transform to log scale
              seasonal=list(order=c(0,0,0),period=12),
              xtransf=data.frame(I911=1*(seq(kota)==46),
                                 I911=1*(seq(kota)==46)),
              transfer=list(c(0,0),c(1,0)))
> air.m1

Call:
arimax(x = log(kota), order = c(3, 0, 0), seasonal = list(order = c(0, 0, 0), 
    period = 12), xtransf = data.frame(I911 = 1 * (seq(kota) == 46), I911 = 1 * 
    (seq(kota) == 46)), transfer = list(c(0, 0), c(1, 0)))

Coefficients:
          ar1     ar2     ar3  intercept  I911-MA0  I911.1-AR1  I911.1-MA0
      -0.0447  0.0686  0.1710     8.1999   14.4892      0.0537    -14.6782
s.e.   0.1255  0.1267  0.1263     0.1023  111.8000      0.4048    111.7594

sigma^2 estimated as 0.4105:  log likelihood = -59.45,  aic = 132.9

ARIMAX 中的标准误差得到 NaN 结果

Standard error in ARIMAX got the NaN result

r

time-series

data-analysis

forecasting

arima