seasonThis 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
Hypothesistesting
Modified ATR Indicator [KL]Modified Average True Range (ATR) Indicator
This indicator displays the ATR with relative highs and relative lows statistically determined.
What is ATR:
To know what ATR is, we need to understand what a True Range (TR) is.
- TR at a given bar is the highest distance between points: a) High vs low, b) High vs Close, and c) Low vs Close.
- ATR is the moving average of TRs over a predefined lookback period; 14 is the most commonly used.
- ATR can be mathematically expressed as:
Why is ATR Important
ATR often used to measure volatility; high volatility is indicated by high ATR, vice versa for low. This is a versatile tool allowing traders to determine entry/exit points, as well as the size of stop losses and when to take profits relative to it.
This is an opinion: Through observations, I have noticed that ATR can also indirectly tell us the levels of relative volume. This intuitively makes sense because in order to increase length of TR, high amounts of capital inflow/outflow is required (graphically speaking, high volume is required in order to make lengths of candle sticks longer). The relationship between ATR and relative volume should hold unless the market is illiquid to the extreme that there is no relationship between volume and price.
That said, knowing the relative lows/highs of ATR is very useful. It can be interpreted as:
- Relative high = high volatility, usually during sell offs
- Relative low = decreasing volume, could indicate price consolidation
Instead of arbitrarily determining whether ATR is high/low, this indicator will determine relative highs and relative lows using a simple statistical model.
How relative high/low is determined by this model
This indicator applies two-tailed hypothesis testing to test whether ATR (ie. say lookback of 14) has greatly deviated from a larger sample size (ie. lookback of 50). Assuming ATR is normally distributed and variance is known, then test statistic (z) can be used to determine whether ATR14 is within the critical area under Null Hypothesis: ATR14 == ATR50. If z falls below/above the left/right critical values (ie. 1.645 for a 90% confidence interval), then this is shown by the indicator through using different colors to plot the ATR line.
