Valid use of repeated measures ANCOVA?

I am running a repeated measures study with four time points. A single group of participants receive the same questionnaire at each time point, which is assessing variable X. I am determining how variable X changes over time. I plan to analyze this in SPSS using a repeated measures ANOVA (with follow-up tests).

Participants are also filling out an additional questionnaire at the beginning of the study (one assessment only). This questionnaire is assessing a continuous variable, which I will call variable Y. I want to see if changes in variable X vary according to variable Y. For instance, perhaps participants scoring higher on variable Y show little or no change in variable X over the four time points, whereas those scoring lower on variable Y steadily increase on variable X over the four time points.

My original plan was to analyze this using a repeated measures ANCOVA, entering variable Y as a covariate (and variable X as the repeated measure). I would be looking at the interaction between X and Y in the output. I am wondering if anyone can tell me whether this is a valid analysis. I am questioning myself because I typically use ANCOVA to control for a covariate (i.e., the covariate is a secondary concern in the analysis); whereas in this case, I am essentially trying to use the covariate as a continuous predictor of X.

Additional details: sample size is N = 80; I am not missing any data for either variable X or Y.
From what I can tell, it seems to be a valid analysis. The key point is that you analyze your within-subjects main effect with a repeated measures ANOVA, and any effects involving your continuous predictor using a repeated measures ANCOVA (i.e., between-subjects effects, as well as within-between interactions). Even though the repeated measures ANCOVA will give you a within-subjects main effect, it will be adjusted by the continuous predictor (which you enter as a "covariate"), at least in SPSS using the GLM menu option. That is why you need to run a separate repeated measures ANOVA for the within-subjects main effect.

I found that these references were useful:

Schneider, B.A., Avivi-Reich, M., & Mozuraitis, M. (2015). A cautionary note on the use of the Analysis of Covariance (ANCOVA) in classification designs with and without within-subject factors. Frontiers in Psychology, 6, article 474. doi: 10.3389/fpsyg.2015.00474

Baguley, T. (2012). Serious stats: A guide to advanced statistics for the behavioral sciences. Basingstoke: Palgrave Macmillan.
Thanks for your fast reply!

So if I understand you correctly, you compare the regular RM ANOVA with the ANCOVA to check if there is a different outcome because of the covariate. And if there is a difference you conclude that there is an interaction?

What I still find odd is that one of the assumptions of the ANCOVA is that there cannot be an interaction between the IV and the covariate. Can this be ignored when comparing the RM ANOVA with the ANCOVA?
No, you use the regular RM ANOVA to assess the within-subjects effect (leave the continuous predictor out of the analysis), and you use the RM ANCOVA to assess the between-subjects effect and the within-between interaction (both of which involve the use of the continuous predictor, i.e., the "covariate"). The RM ANCOVA will also give you within-subjects information in the output, but this should be ignored as it will be inaccurate (you use the results from the RM ANOVA instead). The references that I listed go into greater detail about why this is the case.

Generally with RM ANCOVA there shouldn't be a within-between interaction, as it indicates that the continuous variable that you are using as a covariate will not properly adjust the dependent variable along the within-subjects factor. But in my case, I'm not interested in using the continuous variable as a covariate (i.e., an adjustor; in fact, I don't really want my scores adjusted at all) - this is related to the reason why you use the RM ANOVA to assess the within-subjects effects and not the RM ANCOVA.