Solved – Seasonal component in daily time series remains after stl

rseasonalitytime series

I'm following the procedure in this post (Adjusting daily time series data for the seasonal component) on R 3.2.3 (linux).

The de-seasoning process in the above post works fine. But with my data, a weather time series with 32,000+ observations, the same process leaves behind a noticeable seasonal trend, as shown below.

> ZI_Index <- ts(ZI_FINAL$ZI, start = c(1926,1,1), frequency = 365.25)
> ZI_Trends <- stl(ZI_Index, s.window = "periodic")
> plot(ZI_Trends)

> ZI_Detrend <- ZI_Trends$time.series[,"remainder"]
> monthplot(ZI_Detrend)

> ZI_Detrend_Trends <- stl(ZI_Detrend, s.window = "periodic")
> plot(ZI_Detrend_Trends)

Best Answer

Perhaps you need some sort of hybrid model incorporating memory as well as dummy variables. You might want to look at R Time Series Forecasting: Questions regarding my output although weather data is not impacted by holidays/day-of-the week etc.. Previous day's weather is often a good forecaster for today's weather.

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Solved – Calculate trend slope after STL decomposition

You can't get a "slope" because STL allows for a nonlinear trend. But you can get the numerical values of the trend as follows:

require(fpp)
la10 <- log(a10)
fit <- stl(la10,s.window="periodic")
trend <- fit$time.series[,"trend"]
plot(la10)
lines(trend,col="red")

If you really want a linear trend, then don't use stl(). Instead, fit a linear trend with seasonal factors:

fit2 <- tslm(la10 ~ trend + season)
n <- length(la10)
plot(la10)
lines(ts(fit2$coef[1]+fit2$coef[2]*(1:n)+mean(fit2$coef[-(1:2)]),
  start=start(la10),f=12),col="red")

Then fit2$coef["trend"] gives the slope of the fitted trend.

I've chosen an example where the trend is relatively linear. In many examples, the trend will be non-linear and the linear model approach will not work.

I've ignored the serial correlation in the residuals, so the estimate of the trend is not efficient, but it is still unbiased.

You can do better using Arima() with xreg containing the trend and seasonal dummy variables.

Solved – Significant autocorrelation in time series decomposition random component

So after some research into the algorithms, it seems that neither decompose() nor stl() can handle complex, multiple periods (which otherwise make it through to the remainder component). Like most time series analysis questions, it seems Rob Hyndman has authored the answer to this problem in bats() and tbats() in his forecast package, now I have to learn how to use them properly by wading through his paper that he wrote a few years ago on the algorithm.

Best Answer

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Solved – Calculate trend slope after STL decomposition

Solved – Significant autocorrelation in time series decomposition random component

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