Assessing Volatility Persistence and Stationarity in Return Series
Summary
The document explores how to study volatility in daily stock-price data after calculating log returns. It asks whether stationarity tests such as ADF and KPSS can classify volatility, how to summarize persistence from autocorrelation, and how to compare low, high, and typical volatility periods without fitting ARIMA, ARCH, or GARCH models. The author reports a strongly declining autocorrelation sequence for a series with roughly 3,441 observations and plots values after dividing them by the number of reported lags.
The material is primarily a research question and example rather than a complete analysis or validated procedure. It supplies no resolution of the stationarity-test hypotheses, no statistical criterion for classifying volatility regimes, and no interpretation grounded in a defined volatility estimator. Dividing autocorrelations by the count of reported lags does not itself establish persistence or significance. The document therefore helps frame the issues but leaves the proposed analyses and conclusions open.
Key ideas
- Volatility analysis typically begins with returns derived from price observations.
- ADF and KPSS tests address stationarity, but their hypotheses need to be interpreted in the context of the series being tested.
- Autocorrelation can describe dependence across lags, though a collection of values needs a suitable summary and significance assessment.
- The example reports a declining positive autocorrelation sequence for the studied series.
- The document does not establish a method for labeling low, normal, and high volatility regimes.
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Full text
# Calculate and study volatility time series # Calculate and study volatility time series I am trying to study a time series. I have 10-year daily close prices for some stocks, so my time series is very simple: each day I have a close price for my company. The question is: how can I want to study volatility, so here's what I did: - calculate the log returns - compute volatility From to this point on, I'm lost. Here's some of my ideas, but I need a confront and some advices: - is it statistically good to run ADF test and KPSS test and say "ok, my volatility is stationary / non-stationary"? Which hypothesis should I do (and check) on stationarity? - is it statistically good to compute autocorrelation in order to say "ok, my volatility is persistent/ non-persistent"? I can't really interpret the results I obtain: there are many numbers, but I can't obtain a final result for the whole series. How can I do it? I don't want to have to look at plots to have the final answer, since I will repeat this work for about 100 different time series... - Do you know how can I obtain a confront between low-volatility, high-volatility and normal-volatility? I would like to have a statistical measure or confront, but I cannot find anything (I would like to exclude arima, arch and garch models since I cannot do them). Is it correct to have the three calculated and plotted during the same period? How can I do that? Sorry for the very long and articulated question, but I have been working on this for a while and I really can't find clear tutorials or hints and I am not able to do this alone... EDIT: After a useful comment, here's something I did about autocorrelation a. I computed the autocorrelation function on the time series. From almost 3441 records, I got [1. , 0.98477797, 0.96781082, 0.9514661 , 0.93459373, 0.9176652 , 0.90032963, 0.88131626, 0.85938358, 0.83661734, 0.81445237, 0.79271494, 0.77129042, 0.75047027, 0.72866826, 0.70386183, 0.67833892, 0.65411195, 0.62999035, 0.60672692, 0.58538626, 0.56349308, 0.53889435, 0.51342648, 0.48940659, 0.46608168, 0.44405652, 0.42406814, 0.40413679, 0.38250615, 0.36066609, 0.35314497, 0.34682382, 0.3412075 , 0.3378708 , 0.33433299] b. I divided these results by the lenght of acf results (which is 36), obtaining [0.02777778, 0.02735494, 0.02688363, 0.02642961, 0.02596094, 0.0254907 , 0.02500916, 0.02448101, 0.02387177, 0.02323937, 0.02262368, 0.02201986, 0.02142473, 0.0208464 , 0.02024079, 0.01955172, 0.01884275, 0.01816978, 0.01749973, 0.01685353, 0.01626073, 0.01565259, 0.01496929, 0.01426185, 0.01359463, 0.01294671, 0.0123349 , 0.01177967, 0.01122602, 0.01062517, 0.0100185 , 0.00980958, 0.00963399, 0.00947799, 0.0093853 , 0.00928703] c. I plotted these numbers, getting the result in the image here below. What do you think about it? Do you think it is correct? I'm not sure about how to interpret its meaning, do you have any advice/observation?
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