Hello

My apologies for the inconvenience and thanks a lot for the answers provided!

For 1.2 and 1.3, one common theme was whether the season parameter depended on periodogram of the series' involved or whether it is the frequency at which the data is collected. The details are below:

Sample Data: (Total 62 data points)

Date logdiff logexch 
2003-Jan -1.07173 4.77811 
2003-Feb -1.07496 4.78164 
2003-Mar -1.09263 4.78582 
2003-Apr -1.08933 4.79206 
2003-May -1.09413 4.76149 
2003-Jun -1.09396 4.71402 
2003-Jul -1.09613 4.69993 
2003-Aug -1.09630 4.69711 
2003-Sep -1.10494 4.67488 
2003-Oct -1.08094 4.66070 
2003-Nov -1.09220 4.69236 
Commands used for 1.1:
m1co1 = ca.jo(cor2,type="eigen",ecdet="const",K=2,season=12,spec="transitory")

m2co1 = ca.jo(cor2,type="eigen",ecdet="const",K=2,spec="transitory")

(both resulted in order of cointegration =1 at 5% significance level)

Further, I used conversion command to utilize the capability of VAR for prediction:
vecm.lvl.m1 = vec2var(m1co1,r=1)


and finally used predict(vecm.lvl.m1) command to get the forecast for which I found out the MAPE manually for both the m1co1 and m2co1 models and got the MAPE to be lesser for m2co1 as compared to m1co1. So the question is whether to actually use season parm or not..

Finally, 1.2:
m1co1 = ca.jo(cor2,type="eigen",ecdet="const",K=2,season=2,spec="transitory")
Error in while (nrow(dums) < N) { : argument is of length zero
Now, I dont know whether theoratically 2 is a "correct" value to be passed or not, but it does give above error.

I'm sorry if above doesn't help in improving understanding of my doubts. Thanks again for the explanation, it is just enough helpful so as to allow me to carry on with the work.

Gunjan Narulkar,
Ist Year M. Mgmt., DOMS,
Indian Institute of Science
Contact: +91-99007-40404
LinkedIn: in.linkedin.com/pub/gunjan-narulkar/19/a3b/521


________________________________
 From: Matthieu Stigler <matthieu.stigler@gmail.com>

Cc: "r-sig-finance@r-project.org" <r-sig-finance@r-project.org> 
Sent: Wednesday, June 5, 2013 1:22 PM
Subject: Re: [R-SIG-Finance] Regarding significance of "Season" parameter



Hi

This is the right forum to ask this, not sure though it is the right form ;-) You are asking here many questions, some of which cannot be answered without reproducible code. So let me just answer 1.1 and 2:

1.1: Not the seasonal components refer to deterministic seasonality, not stochastic. So this is nto the same as ARIMA vs SARIMA, since SARIMA concerns stochastic seasonality. There have been some papers on seasonal cointegration (what corresponds to SARIMA), but not very popular, and not implemented in R afaik.
1.2/1.3: not clear or no code to answer

2: yes, you are right, ecdet="const", restricts the constant to enter the coint relationship. 

Best

Matthieu






Hi,
>
>I'm trying to learn about cointegration, specifically about how to use "ca.jo" for finding the cointegration basis. The data is that of FX rates and M1 supply difference. I need help understanding the below two points:
>
>1. Seasonal variables: 
>
>-> What is the importance of season parameter apart from seemingly obvious explanation in the documentation; in other words, should it be understood as equivalent of Seasonal ARIMA vs ARIMA where we take care of the seasonal unit roots? 
>
>-> Should the parameter be set to the value at which the Y_t under question is sampled? Or should it be based on some common frequency derived from individual Y_t component series's periodicity as found from their periodogram (spectrum command in R)?
>
>-> Should the season paramater must be greater then 2? As by spectrum of M1 and FX rate series, I was getting the prominent frequencies for both variables as 2 and its multiples, but got below error, which got resolved as soon as I used anything >2:
>
>"Error in while (nrow(dums) < N) { : argument is of length zero"
>
>Background: I tried checking for cointegration between two monthly series, taking the "season" parameter as 12 (as I had monthly data) first time and without having any season parameter the second. The order of cointegration in both the cases was 1. But further, when I tried fitting VECM and using vec2var created 6 months ahead forecasts and calculated MAPE (Mean Absolute Percentage Error), the MAPE for ca.jo output without season parm specified was better then with season parameter - which lead me to the above confusions.
>f
>
>2. ecdet paramter: 
>The awesome book as well as documentation describe this parameter nicely. But when I use it, the message that comes in the output is a bit confusing:
>
>> cv1.m1.bop = ca.jo(cor2,type="trace",ecdet="const",K=2,season=12,dumvar=bop)
>> summary(cv1.m1.bop) 
>
>
>###################### 
># Johansen-Procedure # 
>###################### 
>
>Test type: trace statistic , without linear trend and constant in cointegration 
>.
>.
>.
>
>The confusion is that I'm interested in finding out presence of "restricted constant", so I used "ecdet='const'". Am I correct in doing so?
>
>Apologies if this is not the right forum for asking these questions and also for the long mail.
>
>Thanks & Regards,
>
>Gunjan Narulkar,
>Ist Year M. Mgmt., DOMS,
>Indian Institute of Science
>Contact: +91-99007-40404
>LinkedIn: in.linkedin.com/pub/gunjan-narulkar/19/a3b/521
>
>_______________________________________________
>R-SIG-Finance@r-project.org mailing list
>https://stat.ethz.ch/mailman/listinfo/r-sig-finance
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>
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