在R中，auto.arima无法捕获季节性

Question

auto.arima() is giving me no seasonal component for my series, even though I can see that there is one present. The function gives me a non seasonal ARIMA model of order (5,0,0). So, when I try to forecast using that model, it just gives the mean. The time series is of daily minimum temperatures in Melbourne, Australia for ten years.

Click this link to see the data and the auto.arima forecast

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library(readr)

temp <- read_csv("~/Downloads/Melbourne Minimum Temp.csv", 
                 col_types = cols(Date = col_date(format = "%m/%d/%y"), 
                                  Temp = col_number()))

t <- ts(temp$Temp, start = temp$Date\[1], end = temp$Date[nrow(temp)])

auto.arima(t, trace = T)

`

Tried using the data as a ts object, as an xts object, and as a vector.

Answer 1

Just reporting a good well explained - as usual - blogpost by Rob Hyndman.

https://robjhyndman.com/hyndsight/dailydata/

The relevant part to your question says (blockquoting exactly the page):

When the time series is long enough to take in more than a year, then it may be necessary to allow for annual seasonality as well as weekly seasonality. In that case, a multiple seasonal model such as TBATS is required.

y <- msts(x, seasonal.periods=c(7,365.25))
fit <- tbats(y)
fc <- forecast(fit)
plot(fc)

This should capture the weekly pattern as well as the longer annual pattern. The period 365.25 is the average length of a year allowing for leap years. In some countries, alternative or additional year lengths may be necessary.

I think it does exactly what you want.

I also tried to simply create the time series with msts

y <- msts(x[1:1800], seasonal.periods=c(7,365.25))

(I cut the time series in half to be quicker)

and then run auto.arima() directly on it, forcing a seasonal component with D=1

fc = auto.arima(y,D=1,trace=T,stepwise = F)

it will take a while.. because I set stepwise = FALSE (if you want it to look at all combinations without shortcuts you can set approximation=FALSE as well)

Series: y 
ARIMA(1,0,3)(0,1,0)[365] 

Coefficients:
         ar1      ma1      ma2      ma3
      0.9036  -0.3647  -0.3278  -0.0733
s.e.  0.0500   0.0571   0.0405   0.0310

sigma^2 estimated as 12.63:  log likelihood=-3854.1
AIC=7718.19   AICc=7718.23   BIC=7744.54

and then the forecast

for_fc = forecast(fc)
plot(for_fc)

I am adding a figure with the complete time series (red) on top of the output of plot(for_fc) and it seems to work decently - but it was just a quick test.