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I have time series data for a 3 month period and need to determine the presence of any statistical trend over time. I thought about dividing the data by month and then testing the hypothesis H0: av.M1=av.M2=av.M3 is this a valid test to determine the presence of a trend?

y-axis would be price and x-axis time so i cannot examine a beta coefficient. Are there any statistical tests to determine a lack of trend in time series data (constant prices over time in this context)?

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  • $\begingroup$ Can you tell us more about the frequency of your data collection schedule? For instance, do you have one value of your time series per day? $\endgroup$ – Isabella Ghement Jul 19 '18 at 1:54
  • $\begingroup$ of course, i have between 4 and 7 observations occurring every day for 90 days. scatter plots show a consistant looking price trend over the period but i wanted to perform a statistical test to validate that there was in fact no significant upward/downward trend $\endgroup$ – Tom Witten Jul 19 '18 at 2:20
  • $\begingroup$ I am using the latest Stata package if that helps :) $\endgroup$ – Tom Witten Jul 19 '18 at 2:21
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    $\begingroup$ yes, multiple observations for each day beggining april 1st an ending june 30th $\endgroup$ – Tom Witten Jul 19 '18 at 9:18
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    $\begingroup$ I could of course compute average daily price and have a singe daily observation if that helps? $\endgroup$ – Tom Witten Jul 19 '18 at 9:19
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I am not aware of a “trend” test. One option you can do is smooth the data, such that you have a fairly good approximation of the mean. Once you have a smoothed mean, you can either eye ball the data to determine this, or try to fit this to some model. Then, use parameter inference (on the size, and direction) on these model parameters for your conclusion.

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  • $\begingroup$ If i wanted to demonstrate that there was no trend at all (constant prices over the 3 months) could i just work out the average monthly price and standard deviation and perform an ANOVA test to accept/reject the null hypothesis that all 3 means are the same? $\endgroup$ – Tom Witten Jul 22 '18 at 12:52
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If you can assume that, other than a possible trend, your data is white noise, you might resort to the (non-parametric, permutation) test described here: TUSELL, F. (2001) A permutation test for randomness with power against smooth alternatives. Statistics and Computing, vol. 11, p. 147-154. I can send you a copy if you have trouble finding the paper.

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