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season

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This script is meant to help verify the existence of a seasonal effect in asset returns, using a Z-test. There are three steps:

1. Think of a way to identify a season. The available methods are: by month, by week of the year, by day of the month, by day of the week, by hour of the day, and by minute of the hour.
2. Set the chart to the unit of your season. For example, if you want to check whether a crop commodity's harvest season has a seasonal implication, select "month". If you want to investigate the exchange's opening or close, select "hour".
3. Using the inputs, select the unit (e.g. "month", "dayofweek", "hour", etc.) and the range that identifies the season. The example natural gas chart has set "start" to 8 and "end" to 12 for September through December.

The test logic is as follows:

The "season" you select has a fixed length; for example, months eight through twelve has a length of four. This length is used to compute a sample mean, which is the mean return of all September-December periods in the chart. It is also used to calculate the mean/stdev of every other four-month period in the chart history. The latter is considered the "population." Using a Z-test, the script scores the difference between the sample returns and the population returns, and displays the results at two levels of significance (P = 0.05 and P = 0.01). The null hypothesis is "there is no difference between the seasonal periods and the population of ordinary periods". If the Z-score is sufficiently large or small, we can reject the null hypothesis and say that there is a seasonal effect at the given level of confidence. The output table will show green for a rejection of the null hypothesis (meaning there is a seasonal effect) or red of acceptance (there is no seasonal effect).

The seasonal periods that you have defined will be highlighted on the chart, so you can make sure they are correct. Additionally, the output table shows the mean, median, standard deviation, and top and bottom percentiles for both the seasonal and population samples.

Many news sites, twitter feeds, influences, etc. enjoy posting statistics about past returns, like "the stock market has gone up on this day 85 out of the past 100 years" and so on. Unfortunately, these posts don't tell you that many of these statistics are meaningless, as even totally random price fluctuations will cause many such interesting figures to occur. This script provides a limited means of testing some such seasonal effects so you can see if they are probably just random, or if they may have some meaning.

Note that Tradingview seems to use 1-based indexing for daily or higher timeframes, and 0-based indexing for intraday timeframes:

Months: 1-12
Weeks: 1-52
Days (of month): 1-31
Days (of week): 1-7
Hours (of day): 0-23
Minutes (of hour): 0-59
發布通知: - added an option (disabled by default) to label each season's return. however, it doesn't seem to work very well for some reason... beta feature!
發布通知: corrected sampling distribution
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