# Tag Info

## Hot answers tagged stationarity

### Estimate covariance matrix using prices

If you assume that a financial asset price has a change that is a wiener process then you can view the future value of that asset as the initial value plus the sum of the independent daily changes (...
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### Are cumulative returns stationary?

Hi: Even if returns were stationary ( which is probably dependent on the time series one is considering ), cumulative returns, where $n$ is not fixed ( as it in say a rolling sum with a fixed window ...
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### log return of sp500. Stationary vs strictly stationary

We can talk about whether a strictly stationary or weakly stationary process might usefully describe that data. My answer to both would be yes. I also have issues with other text that people have ...
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### Differencing vs Detrending financial time series

Hi: It depends on what the DGP of the original process is. Is the process trend stationary or difference stationary ? If it's trend stationary then de-trending is the way to go. If it's difference ...
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### Does predictability in a VAR process imply mean reversion or momentum?

The point of confusion may be in thinking that a predictable price process is synonymous with a mean-reverting process while using the definitions in these papers, it's actually the opposite! In the ...
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### Are cumulative returns stationary?

Stock prices are definitely not stationary as tomorrows closing price is strongly influenced by today's closing price and prices tend to change. Returns can be potentially stationary and are therefore ...
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### Transforming a time series

Fractional differentiation (or differencing) is a technique that transforms an input series to a stationary series while retaining "long-term" memory. Consider the following example based on ...
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### How to use autocorrelation plot to interpret time series data?

Just by looking at the graphs, I'd say: Unit root Constant series Seasonality AR model No AC No AC
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### Issues making series stationary

Your shift is in the wrong direction. Do this: df.price = pd.to_numeric(df.price) df['logret'] = np.log(df.price/df.price.shift(1))
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### Does Weak stationarity imply ergodicity ?

Ergodicity is connected to mixing, meaning there is one limiting distribution and it is used for time averages too. If you take a process in the real numbers that starts at a random value and then ...
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### Stationary Process with autocorrelation in Variance; square root rule

You are correct in that the series is not stationary. The ADF test isn't designed to test for stationarity outside the center of location. You are not going to be able to use the square root rule to ...
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### Does forecasting asset returns by default assumes non-stationarity of asset returns?

This looks confused? I don't understand what you're saying in the second paragraph... Comment 1: "Best" forecast depends on what you mean by "best." Let $Y$ be a random variable and $\mathcal{F}$ be ...
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### Would you consider yield a stationary or non-stationary process?

Following Meucci (Risk and Asset Allocation book, page 112-113) you should use "change of yield to maturity" (simple change, not percentage) since they represent Fixed IncomeÂ´s invariant. Change of ...
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### Estimate covariance matrix using prices

For the same reason you can't meaningfully measure covariance/correlation using price of individual assets...correlation (covariance by extension) represents the comovement in deviations from ...
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