I just have a few questions regarding applying the Box-Pierce Q statistic.

I have 52 data points on which i fit a variety of ARIMA models.

To test if the residuals of the model form a white noise, i use the Q statistic:

When i take 1st and 2nd differences i'm essentially left with fewer data points.

So do i still use T=52, or do i use T=50 for the 2nd differenced Time Series?

[NEAS: T = 50]

Also, the Q statistic has (K-p-q) degrees of freedom.

But if i fit an AR(2) model with an annual lag term for seasonality (making the model AR(12)), then what is the value of p?

Is it 12 or 2 or 3?

[NEAS: 3]

I am doing my project on number of house sales in US.  I have started work as shown in the Excel file.  The data seems to have seasonal influence as well as being nonstationary.  It also appears that the time series is seasonal with 12 month lags.  I have computed the Autocorrelations, but I am not sure where to go next.  How do I compute the parameters for an AR model?  Any advice as to what to do next would be very helpful.  Thanks!

[NEAS: Use Excel's regression add-in. Even if you use a 12 month seasonal lag, you may have just 2 or 3 lags: 1 month, 2 months, and 12 months. You would not use every lag from 1 to 12 months.]

I want to do a Durbin-Watson test on an ARMA(1,1) series, but I only know how to use Excel regression on AR(1), AR(2), etc to get the residuals.

But there are some examples of student projects that got the values, but they didn't mention using Minitab or something else, so I assumed they used Excel.

Any ideas?

Thanks for any help.

 

Hi NEAS, I need help on my student project. I'm trying to do a time series on points scored per game for a player, and this player played different number of games per season. Now I see that there is seasonality in the scoring, but how do I unseasonalize? The Chapter 10 in the cryer chan text mentions seasonal models, Yt-Yt-12. But the games are not in order 12 or any order in fact (say he plays games 1,2,5,8,9,12... etc in one season, no matter what Yt-n is, I cannot remove seasonality with this method)

What other methods of unseasonalize are there?

[NEAS: Use only the games he played: if he plays 40 games in one season and scores 400 points and 80 games in another season and scores 600 points, his points per games are 10 and 7.5; for longer term cycles, one needs time series models with more lags.]

1) I don't understand how Excel got to the predicted Y when I use the regression add in to calculate AR(1). It does not match the forecasted Y(1) using the intercept and X variable 1 they give. I can see that the residual is just predicted Y - actual. But I need to know how excel arrived at the predicted Y in order to do the Durbin Watson and Box Pierce Q tests on the Time Series Techniques given to us on the excel files.

[NEAS: Excel's regrssion add-in does basic linear regression. Try the add-in for a simple data set of 3 points where you know the proper answers, and check to see that you are using the add-in correctly.]

2) Related to 1) Since we are supposed to use the excel's residuals to form DW and BP-Q tests, how do I get the residuals for MA(1)? Same for ARMA(1,1)

[NEAS: Assume residual for the first period is 0; work out subsequent residuals from the MA(1) or ARMA(1,1) process.

3) Is Bartlett's test needed? I see a lot of sample projects with this test, but I do not see where the instructions are on how to use it.

[NEAS: Barlett's test says that the residuals from a correct model are white noise with a normal distribution whose variance is T/N.]

Actually this is a similar question to Seattleact's previous post. But no answer was given there...

My previous question on seasonality was probably not clear. I'm asking lets say I have temperature data, and I know there is seasonality. If I have data for every month, the seasonality is easy to get rid of, was can subtract Yt-12 from Yt. However, let's say you have data for 4 years. Year, you are missing data on February and March. Year 2 you are missing data from May, Year 3 you are missing data from December, year 4 you are missing the last half of the year. So I have a total of 38 data points. Or 48 data points with 10 data points of 0. Now lag 13, which is 12 lags after lag 1, is not January, it is March. How do I unseasonalize these temperatures?

Are you saying that I should just get an average of every month and an average of the year and then just subtract from each month the difference? Because that would make some sense.

[NEAS: With missing data points, time series analysis is more difficult. Your proposed method is fine; other methods can also be used. Alternatively, instead of the 0's, you can use the monthly averages for the missing values.]

OK, For the question on Excel's predicted Y. I tried a simple X = 1,2,3,4 Y = 2,4,6,8 and excel's regression does give me a simple linear regression equation of intercept 0 and x coefficient 2. This is good, but on the time series techniques excel file, on the BPQS tab, the regression results used on that page (B85:B125) is definitely not using simple regression of y=b0+b1Yt. The predicted Y there goes to 5 then back to 4 then 5 again, which is not linear. I had thought that this was the forecasting equation for AR(1)

Y(1)=mu+phi(Yt-mu)

but that did not fit the lines either with mu = intercept = 0.2486 and phi = x coefficient = 0.9531. I really don't understand how excel is getting these predicted Y. Am I being stupid here?

OK, after a few days of looking online, I finally found that I can replicate the excel's predicted Y by using the =Forecast() function and use X as the values being forecasted. But I still cannot figure out how to make a predicted Y (or residuals)for MA(1) process. What do you mean when you say assume the residual is 0 for period 1 and then work it out? Certainly, it is not the MA(1) forecasting equation we learned in Time series, as that ends after lag 1. Do I use random number functions and just plot that? How does this work?

NEAS, I have a question:

In fitting AR(1), AR(2), etc, models to temperature data, do we fit the AR model to the deseasonalized data, or to the smoothed/original temp data?  I had been under the impression we fit to the deseasonalized data and then added it back to the daily average to get the "expected".  But from a couple of the samples it doesn't seem to be that way.  Which is the right way to go about it?  Thanks!

[NEAS: You have several options. The posting on seasonality (in the student projects discussion forum) expains them. The method depends on the reason for seasonality, such as weather vs holidays. See

VEE Time Series Student Project

» Time Series Project Templates

Seasonality: Project Template ...]

I've seen a few project samples where students compare the autocorrelation of a specified AR(p) model to the sample ACF for the time series with K values . If I understand correctly, the model autocorrelation is just the correlation between the predicted values specified by the model at lags 1 to (K-p). As such, the predicted series would actually correspond with terms 2 through term K of the original time series. My question is whether the autocorrelation of the model should be compared to the original time series sample acf or with a modifed version of the sample acf that omits the first p terms of the original time series?

[NEAS: Your question is good. Comparing with the original time series says: does the model represent the empirical data? Omitting the first p terms says: does the model predict well? In most cases, we ask the first question, so we compare with the original time series.]