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Time series analysis (TSA) for quasiperiodic data by using polynomial regression, seasonal decomposition and signal decomposition techniques

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Dataset

Data is generated by using Quasiperiodic function and additive noise

Polynomial Regression

Polynomial regression model for a single predictor, X, is:

image

where h is called the degree of the polynomial. For lower degrees, the relationship has a specific name (i.e., h = 2 is called quadratic, h = 3 is called cubic, h = 4 is called quartic, and so on). Although this model allows for a nonlinear relationship between Y and X, polynomial regression is still considered linear regression since it is linear in the regression coefficients β1, β2,..., βh!

https://online.stat.psu.edu/stat462/node/158/#:~:text=Although%20this%20model%20allows%20for,.%20.%20.%20%2C%20%CE%B2%20h%20

https://stats.stackexchange.com/questions/92065/why-is-polynomial-regression-considered-a-special-case-of-multiple-linear-regres

Trend and Seasonality Analysis

Polynomial regression:

Lineer Regression Assumption: data = model + noise

Noise is a kind of gaussian or normal distribution so we need to check the residual by using the normality test (Shapiro-Wilk) but first let's look at trend.

image

Statsmodel:

Seasonal decomposition

Hodrick-Prescott trend, cycle filter

Signal Decomposition and Time - Frequency Analysis

Emprical Wavelet Transfrom

The main idea is to extract the different modes of a signal by designing an appropriate wavelet filter bank. This construction leads us to build adaptive wavelets called the empirical wavelet transform.

https://ieeexplore.ieee.org/document/6522142

https://github.com/HarishBachu/StockPrediction

Singular Spectrum Analysis

In time series analysis, singular spectrum analysis (SSA) is a nonparametric spectral estimation method. It combines elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing.

https://en.wikipedia.org/wiki/Singular_spectrum_analysis

https://ui.adsabs.harvard.edu/abs/2019GeoJI.217..748P/abstract

https://github.com/dmarienko/chaos/blob/master/SSA_for_stock_prices_prediction.ipynb

Notes:

PEP-8 coding style is used for the codes.

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Time series analysis (TSA) for quasiperiodic data by using polynomial regression, seasonal decomposition and signal decomposition techniques

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