In the realm of time series analysis, a stationary series is one whose statistical properties, such as mean, variance, and autocorrelation, remain constant over time (think of a sine wave plot).
On the contrary, a non-stationary time series exhibits changes in these properties, leading to trends, seasonality, or varying volatility. In financial time series analysis, most of the data sets, such as stock prices or economic indicators, are inherently non-stationary. These series often showcase trends, wherein the prices might be increasing or decreasing over time, or seasonality, where patterns repeat over specific intervals.
When it comes to MEM (Maximum Entropy Method) and its application in spectral analysis for financial time series, stationary data is crucial for accurate and reliable results. MEM operates under the assumption that the time series is stationary, meaning it presumes the statistical properties of the series remain constant.
When applied to a non-stationary series directly, MEM might produce misleading results, as the underlying assumptions are violated. This is particularly problematic in financial time series analysis, where the ultimate goal is often to make accurate predictions about future price movements or to uncover the hidden periodicities in the data for better investment/trading strategies.
To address this issue, a common practice is to transform non-stationary financial time series data into a stationary form before applying MEM or any other spectral analysis techniques.
Techniques such as differencing, detrending, or even more sophisticated methods like wavelet transformations (see our Time Series Decomposition tool for TradingView) can be applied to remove trends and make the variance constant.
Transforming the data helps in stabilizing the mean and variance, making the series stationary and subsequently, making the application of MEM more valid and the results more reliable. This pre-processing step is crucial as it ensures that the insights drawn from MEM power spectrum or the forecasts generated are grounded in the actual dynamics of the financial market, rather than being artifacts of non-stationarity in the data.
When it comes to forecasting with MEM, a recommended approach is to use a low-pass filter such as a moving average as a proxy for the price action you are attempting to forecast. This will eliminate a lot of the higher-frequency 'noise' and reduce the overall complexity.
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