# simple multivariate question

#### jbc165

##### New Member
I have, I think, a simple question about multivariate statistics, and I'm not sure which test (or even what kind of test does this).

I have 40 items (replicates) THEY ARE NOT IN ANY PARTICULAR GROUPS. For each item I have tracked the prices each week for a year. So I have 52 measurements of each item. I expect the price of each item to fluctuate seasonally. I want to ask the simple question, "Does the price change over time?"

Because each measurement is not independent, I didn't think I should use ANOVA. I thought I should use MANOVA here, but I am a little confused, because there are no "treatments".

I am confident that the prices change over time. Next, I'll want to know when. Is there a post-hoc analysis to see when the prices tend to go up or go down. Again, I expect the prices to change seasonally.

#### CB

##### Super Moderator
This looks like a time series analysis question. Are you interested in looking at price changes in the individual items separately? (i.e. some may go up and some down over time) And are you interested in testing the evidence for a trend (upwards or downwards) in prices, or something else?

#### jbc165

##### New Member
Cowboy bear,

I am not interested in changes in the individual items. I simply want to see if there is a seasonal (time) trend of OVERALL prices.

For example, the items I am looking at may cost $0.01 or$300, but I expect they may get really high ($0.02 or$500, respectively) during certain times of the year. I don't care about INDIVIDUAL item prices, I just need to control for variation in the individual items. Does that make sense to you? Any analyses you suggest?

#### derksheng

##### New Member
Maybe stationarize the data by taking the log return and then use R_i = a + b*D + error, where D is a dummy that's equal to 1 over the period where the prices are supposed to rise? Then find the number of |t| that are > 1.96 over all the different series? (the b estimate should be significant and slightly positive if your suspicions are correct).

You definitely can't use the prices in multivariate OLS as they're non-stationary so you'll get spurious results.

#### noetsi

##### Fortran must die
It is not really a good idea to determine seasonality with one years of data. You can not be sure that seasonality is really occuring (or there is no trend in it). You should look at several years of data for that.

The problem with repeated measure ANOVA is that it assumes the data has no serial autocorrelation. That is a doubtful assumption with time series. ARIMA is one way to go although it takes a while to learn.

There are many tests for stationarity, Dickey-Fuller test is one example. The most common way however, is just to eye the raw data. If you think there is a trend (which can occur in seasonality or in the non-seasonal data or both) then you can difference it. R or SAS does this or you can do it manually.

#### CB

##### Super Moderator
jbc165, I do think you may need to do some reading about time series analysis. Working with time series data can be quite complex - this isn't a simple question, and trying to approach it with the usual multivariate "toolbag" for cross-sectional data is not going to work. As one major issue, you need to make sure that you understand the distinction between trend and seasonality, and be clear on which you're actually interested in. A good possible reference text to start with could be Time series analysis with R, by Cryer and Chan.