# [R] Regression of a time series on its Quarters

Achim Zeileis Achim.Zeileis at uibk.ac.at
Thu Mar 18 18:11:26 CET 2010

```On Thu, 18 Mar 2010, Gabor Grothendieck wrote:

> Try this:
>
> lm(a.ts ~ factor(cycle(a.ts)) - 1)

An equivalent but somewhat more convenient interface is available in
"dynlm" where you can say dynlm(a.ts ~ season(a.ts)) or
dynlm(a.ts ~ season(a.ts) - 1):

R> dynlm(a.ts ~ season(a.ts))

Time series regression with "ts" data:
Start = 1947(2), End = 2000(4)

Call:
dynlm(formula = a.ts ~ season(a.ts))

Coefficients:
(Intercept)  season(a.ts)Q2  season(a.ts)Q3  season(a.ts)Q4
0.03069         0.01310        -0.19455         0.09481

Best,
Z

>
> On Thu, Mar 18, 2010 at 12:30 PM, Len Vir <lenvir at gmail.com> wrote:
>> # Dear List,
>>
>> # I want to characterize a time series according to its Quarter components.
>>
>> # My data ("a.ts":
>>
>> #                 Qtr1          Qtr2          Qtr3          Qtr4
>> #   1948 -0.0714961837  0.0101747827  0.0654816569 -0.0227830729
>> #   1949 -0.1175517556  0.1151378692  0.1015777858 -0.1971535900
>> #   1950  0.0716002123  0.2551020416  0.0977574743 -0.0739337411
>> #    ...
>>
>>
>> #  The time series is 216 long
>>
>> #  The easiest way I could figure out, is to create
>> #  Quarter dummies:
>>
>> Q1 <- rep(c(1,0,0,0),54)
>> Q2 <- rep(c(0,1,0,0),54)
>> Q3 <- rep(c(0,0,1,0),54)
>> Q4 <- rep(c(0,0,0,1),54)
>>
>> qtr <- cbind(Q1,Q2,Q3,Q4)
>>
>> # and then regress my data on the dummies.
>>
>> summary(lm(a.ts ~ qtr - 1))
>>
>> # The regression on 'Quarters' works fine.
>> # It does exactly what I want it to do.
>>
>> # But!  Surely there must be a more elegant way
>> #       to accomplish the same thing ?!
>>
>> # I have looked at the following packages (amongst others):
>> # tseries, timeSeries, TSA, AER, fSeries, vars, FinTS, xts, fArma,
>> # fRegression, tsfa, uroot, urca, ...
>>
>> # without finding anything more convenient (simpler, nicer!).
>>
>> # Any suggestion?
>>
>> # Thank you.
>>
>> # Len Vir
>>
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