为什么 predict(model, h=2) function 返回 NA 值（模型来自 R auto.arima()）？

Question

This R code predicts sp500 with arima model,

rm(list=ls())
load("StockData.Rdata")
library(seasonal)
library(forecast)
library(tseries)
library(astsa)
sp500 = StockData[,1]
model = auto.arima(sp500,
                     max.p=52,max.q=52,max.d=52,
                     seasonal = TRUE,
                     lambda = "auto", biasadj = TRUE)
predict = forecast(model,biasadj=TRUE, h=2)

Here, I want to use auto.arima with Box-Cox transformation, so I set lambda = "auto" , and biasadj = TRUE . However, the predicted value has mean NaN :

> forecast(model,biasadj=TRUE, h=2)
    Point Forecast      Lo 80     Hi 80      Lo 95     Hi 95
209            NaN -0.1278079 0.1206801 -0.1962931 0.1890652
210            NaN -0.1278079 0.1206801 -0.1962931 0.1890652

I have checked some GitHub questions and some people say that it is because there is NA value in the residual so the point forecast is NaN. However, the residual in model doesn't contain NaN so it should not be the case. So, how can I solve that?

Also, why is the predicted value same for t=209 and t=210?

Answer 1

I have a feeling there is a misunderstanding about what biasadj does, but I think you need to take a step back and inspect the original data.

Let's plot sp500 :

library(ggplot2)
ggplot(data.frame(x = seq_along(sp500), y = sp500), aes(x, y)) +
    geom_line()

A cursory inspection suggests no seasonality and no drift/linear trend; there may be some indication of heteroskedasticity which may warrant a Box-Cox transformation.

Keeping model parsimony in mind, I would start with a default call to auto.arima allowing for a automatic Box-Cox transformation

library(forecast)
model <- auto.arima(sp500, lambda = "auto")
#Series: sp500 
#ARIMA(0,0,1) with non-zero mean 
#Box Cox transformation: lambda= 0.7637886 
#
#Coefficients:
#    ma1     mean
#-0.1142  -1.3103
#s.e.   0.0582   0.0041
#
#sigma^2 estimated as 0.00548:  log likelihood=308.93
#AIC=-611.86   AICc=-611.77   BIC=-601.18

auto.arima determines the optimal model to be ARIMA(0,0,1) on Box-Cox-transformed data with lambda = 0.76, which corresponds to a simple first-order moving average model MA(1). This seems to be consistent with the earlier visual assessment.

When forecasting, forecast will automatically show estimates on the original scale, see eg

autoplot(forecast(model, h = 10))