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?

**Answer**

Are you doing the regression on the data after you’ve *removed* the trend? You have a positive trend, and your seasonal signature is likely masked in your regression (variance due to trend, or error, is larger than due to month), unless you’ve accounted for the trend in Yvar…

Also, I’m not terribly confident with time series, but shouldn’t each observation be assigned a month, and your regression look something like this?

```
lm(Yvar ~ Time + Month)
```

Apologies if that makes no sense… Does regression make the most sense here?

**Attribution***Source : Link , Question Author : mattiace , Answer Author : danno*