I use the decompose
function in R
and come up with the 3 components of my monthly time series (trend, seasonal and random). If I plot the chart or look at the table, I can clearly see that the time series is affected by seasonality.
However, when I regress the time series onto the 11 seasonal dummy variables, all the coefficients are not statistically significant, suggesting there is no seasonality.
I don't understand why I come up with two very different results. Did this happen to anybody? Am I doing something wrong?
I add here some useful details.
This is my time series and the corresponding monthly change. In both charts, you can see there is seasonality (or this is what I would like to assess). Especially, in the second chart (which is the monthly change of the series) I can see a recurrent pattern (high points and low points in the same months of the year).
Below is the output of the decompose
function. I appreciate that, as @RichardHardy said, the function does not test whether there is actual seasonality. But the decomposition seems to confirm what I think.
However, when I regress the time series on 11 seasonal dummy variables (January to November, excluding December) I find the following:
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5144454056 372840549 13.798 <2e-16 ***
Jan -616669492 527276161 -1.170 0.248
Feb -586884419 527276161 -1.113 0.271
Mar -461990149 527276161 -0.876 0.385
Apr -407860396 527276161 -0.774 0.443
May -395942771 527276161 -0.751 0.456
Jun -382312331 527276161 -0.725 0.472
Jul -342137426 527276161 -0.649 0.520
Aug -308931830 527276161 -0.586 0.561
Sep -275129629 527276161 -0.522 0.604
Oct -218035419 527276161 -0.414 0.681
Nov -159814080 527276161 -0.303 0.763
Basically, all the seasonality coefficients are not statistically significant.
To run linear regression I use the following function:
lm.r = lm(Yvar~Var$Jan+Var$Feb+Var$Mar+Var$Apr+Var$May+Var$Jun+Var$Jul+Var$Aug+Var$Sep+Var$Oct+Var$Nov)
where I set up Yvar as a time series variable with monthly frequency (frequency = 12).
I also try to take into account the trending component of the time series including a trend variable to the regression. However, the result does not change.
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3600646404 96286811 37.395 <2e-16 ***
Jan -144950487 117138294 -1.237 0.222
Feb -158048960 116963281 -1.351 0.183
Mar -76038236 116804709 -0.651 0.518
Apr -64792029 116662646 -0.555 0.581
May -95757949 116537153 -0.822 0.415
Jun -125011055 116428283 -1.074 0.288
Jul -127719697 116336082 -1.098 0.278
Aug -137397646 116260591 -1.182 0.243
Sep -146478991 116201842 -1.261 0.214
Oct -132268327 116159860 -1.139 0.261
Nov -116930534 116134664 -1.007 0.319
trend 42883546 1396782 30.702 <2e-16 ***
Hence my question is: am I doing something wrong in the regression analysis?
decompose
function inR
is used). $\endgroup$ – Richard Hardy Mar 12 '15 at 14:23decompose
function, it seems that the function does not test whether there is seasonality. Instead, it just obtains averages for each season, subtracts the mean and calls this the seasonal component. So it would produce a seasonal component regardless of whether there is true underlying seasonal component or just noise. Nevertheless, this does not explain why your dummies are insignificant though you say the seasonality is visible from a plot of the data. Could it be that your sample is too small to get significant seasonal dummies? Are they jointly significant? $\endgroup$ – Richard Hardy Mar 12 '15 at 14:30