'trend' predictor in time-series modelling

[thai1491]

Dear everyone,

I have a small question regarding the role of 'trend' predictor in tslm() function. As explained in Hyndman and Athanasopoulos (2020): "A linear trend can be modelled by simply using x1,t = t as a predictor," where t is the time unit of the time-series.

However, when I try to use trend in time to predict performance in the dataset 'mens400', using trend as a predictor provides a suspicious result:

b2 <- tslm(mens400 ~ trend, data = mens400)

b2$coefficients[2]
trend
-0.2582954

Using time(mens400) makes the result seem more reasonable:

b2.time$coefficients[2]
time(mens400)
-0.06457385

From the authors' explanation, I expected the trend predictor to perform exactly as the time() function but it actually not. Can someone explain what is happening here?
Thank you,
Thai.

[robjhyndman]

The trend term in tslm() will create a predictor equal to (1,2,3,...). But time(mens400) will create a predictor equal to (1896,1900,1904,...) because the Olympics are held every four years. So the coefficient of time(mens400) will be 1/4 of the coefficient of trend. Note that -0.2582954/4 = -0.06457385.

[thai1491]

thank you so much! It makes sense now