Time Series Analysis in Python

Choose Python for time series analysis and learn why it suits data science; install Anaconda, Python 3, Jupyter Notebook, and the relevant packages to set up your coding environment.

Explore why Python and Jupyter are favored in data science for being open source and free to use, cross-platform, high-level, general-purpose tools with notebook workflows.

Install the Anaconda distribution to get Python, the Jupyter Notebook app, and essential data science packages; choose Windows, Mac, or Linux, and install Python 3 with 64-bit as default.

Explore the Jupyter dashboard and file management, including selecting, renaming, uploading, and creating notebooks in the IPython notebook format, with an interactive shell to write code and view output.

Explore how to set up python libraries for time series analysis using Anaconda, including numpy, scipy, and pandas. Install statsmodels, arch, matplotlib, and seaborn via the Anaconda prompt and pip.

Define time series data and distinguish it from other data, explain constant frequency and values attached to a time period, and illustrate seasonality with weather and finance examples.

Understand time series notation: use X and T for period, and t for a single point. Denote prices as X(T) or X_t, with past and future as t-1 and t+1.

Explore the peculiarities of time series data, including identical intervals, missing values, and data aggregation. Forecast future values by maintaining chronological order, handling imputation, and performing pre-processing and Python coding.

Load and prepare time series data in Python by opening Jupyter notebook, importing numpy and pandas, reading index 2018 csv file into a dataframe, and preserving the raw data.

Plot each time series in the data, name graphs with titles, and adjust figure size to compare S&P 500 and FTSE trends; prepare for density and q-q plots.

Explore the q-q plot and how it tests whether a data series follows a normal distribution in time series analysis, using the red diagonal line to assess deviations for forecasts.

Convert the date column from strings to date time values with pandas to_datetime, date_first set to true, so you can describe time period and use the index for time series.

Set frequency with pandas asfreq to create a time series. Use codes like H, W, D, M, A, and B for hourly to business-day data, and address missing values.

Fill missing values in time series with fillna, using forward fill, backward fill, or mean imputation. Verify with isna and sum on series like S&P and Dax.

White noise is a time series with constant mean and variance, no autocorrelation, and thus lacks predictability; compare it to S&P data via plots.

Explore the random walk concept, where prices equal yesterday plus a white noise residual, and compare it with white noise using plots and data in Python.

Explore stationarity in time series analysis, focusing on weak form covariance stationarity with constant mean, variance, and lagged covariance, illustrated by white noise, and distinguish strict from covariance stationarity.

Determine whether a time series is stationary using the Dickey-Fuller and augmented Dickey-Fuller tests in Python, interpreting test statistics, p-values, and lags to assess stationarity.

Define seasonality as cyclical patterns and show how to decompose a time series into trend, seasonal, and residual parts using additive or multiplicative models, noting no seasonality in S&P prices.

Analyze how autocorrelation reveals links between past and present values in time series, preserving chronology and using lagged comparisons like yesterday versus today and year-to-year patterns.

Explore the autocorrelation function (acf) to analyze time dependencies by plotting up to 40 lags with the TSR plots package, and assess significance against white noise.

Learn how the partial autocorrelation function (pacf) isolates direct effects in a time series and compare it to the ACF using 40 lags and ols to plot for S&P 500.

Select the best time series model by starting simple, expanding only if coefficients differ from zero, comparing AIC and BIC, and ensuring residuals resemble white noise.

Explore the ACF and Pacf of prices to select the relevant lags for an AR model, using Footsie values and plots to interpret significance and monthly cycles.

Fit a simple autoregressive AR(1) model to the FTSE market value series using the statsmodels Arma method, estimating C and phi1 and testing significance with p-values.

Fit autoregressive models with multiple lags and compare them via the log-likelihood ratio test to improve predictions, interpreting coefficients and p-values while avoiding overfitting and considering stationary data.

switch from prices to returns to achieve stationarity, test with the augmented dickey-fuller test, compute percentage changes via pct_change, and prepare for acf/pacf analysis.

Examine the ACF and PACF of FTSE returns to interpret how past values relate to current ones, noting significant negative early lags and a simple R model for predicting returns.

Fit an ar(1) autoregressive model to index returns, define the specifications in a notebook. Interpret results showing p-values above 0.05 and explore higher lag models.

Fit higher-lag ar models for returns, assess coefficient significance with log-likelihood ratio tests, and compare information criteria to select the best model.

Normalize time series to a percentage of the first value to compare performance, assess stationarity with the augmented Dickey-Fuller test, and compare normalized returns for unbiased investment insights.

Fit autoregressive models for normalized returns and compare with non-normalized results. Normalization does not change model selection; AR six remains the best.

Extract and analyze AR residuals for prices and returns, test stationarity with Dickey-Fuller, assess white noise via ACF, and compare R7 for prices with R6 for returns.

Compare autoregressive models' slow adjustment to big shocks with moving average models that absorb past residuals and quickly adjust to non-stationary or random walk data.

Explore moving average (MA) model for time series, including its connection to AR models and residuals. Use the ACF plot to determine lag selection and understand coefficient constraints for stability.

Fit a ma(1) model to returns with the Statsmodels tsa arma model, handle missing values, and interpret significant lags from the acf to assess model adequacy.

Fit higher-lag ma models for returns, compare coefficients and log-likelihood across ma2 to ma8, guided by acf, and select the best predictor via significance tests and residual analysis.

Extract eight residuals from the eight-lag MA model for returns analysis. Assess mean and variance, test stationarity with the Dickey-Fuller test, and examine ACF for white-noise behavior and model adequacy.

Explore moving average models for normalized returns, use ACF to pick MA6 or MA8, compare coefficients with non normalized data, assess residuals, and test on non stationary data.

Examine how moving average models perform on prices and why MA(1) struggles with non-stationary data. Conclude that combining AR and MA elements can better model prices and non-stationary processes.

Combine past values and past errors with ARMA in Python to improve predictions by accounting for residuals and shocks beyond AR or MA alone.

Explore the arma model, where current values depend on past values and residuals. Grasp phi and theta, the p and q orders, and why coefficients stay between -1 and 1.

Fit a simple arma(1,1) model to returns using one past value and one past error term, then interpret the coefficients and perform a log likelihood test.

Explore fitting higher-lag ARMA models for returns by starting with an overparameterized AR and MA, then pruning lags based on significance, ACF and PACF guidance, and information criteria.

Explore fitting higher-lag ARMA models for returns, compare ARMA(3,2) and ARMA(2,3), and assess coefficient significance, mean-zero behavior, and model selection via likelihood tests.

Compare higher-lag arma models for returns, using log-likelihood ratio tests to favor arma 3-2 with all coefficients significant, and guide residuals analysis.

Analyze arma residuals by extracting them, plotting their acf, and testing for randomness; compare arma(5,1) with arma(3,2) using log-likelihood and aic to pick the best model.

Analyze arma models on non-stationary price data, compare to returns, assess residuals with acf and pacf, and select arma five six or arma six one models using log-likelihood and aic.

Learn how ARIMA models extend ARMA to non-stationary data by differencing to achieve stationarity, modeling differences or returns rather than prices, with applications to market indices like the FTSE.

Grasp the intuition and notation of ARIMA models, with P, D, Q orders, and learn how differencing turns non stationary prices into a stationary ARMA-like series.

fit a simple arima model for prices, import arima from Statsmodels tsa arima model library, set p d q to one, examine coefficients and residuals, and review acf for guidance.

Compare higher-lag ARIMA models (111, 113) by significance at 5% level, log likelihood, and AIC to select the best, then validate with residual ACF.

Compare higher-lag ARIMA models for price returns, evaluate 113, 613, and 511 using log-likelihood and AIC, and conclude ARIMA 511 as the best estimator while analyzing residuals.

Explore higher levels of integration in time series analysis using Python, test for stationarity with augmented dickey-fuller test, and compare Arima models with delta prices differences.

Explore why ARIMA models are not ideal for non-stationary data like prices, but why they're used for returns with integration trade-offs, including data attrition, computational cost, convergence issues, and interpretability.

Explore how ARIMAX extends ARIMA with exogenous variables in Python, specify X for time-varying or categorical factors, and test S&P prices as exogenous to improve model fit.

Explore seasonal time series with SARIMAX, learning how seasonal orders P, D, Q and cycle length s capture recurring patterns alongside non-seasonal ARMA terms, including exogenous variables.

Identify volatility by focusing on the magnitude of residuals, squaring values to ignore sign, and apply arch models to measure conditional volatility and stability based on past data.