Master Financial Econometrics for Time Series Analysis

Explore how to model financial returns using ln returns, build histograms to visualize distributions, and interpret tails and density for probability-based forecasting.

Discover reliable sources for financial time series data, including Kaggle datasets and crypto exchange APIs, exportable to Excel with OHLCV fields for consistent course analysis.

This lecture offers a ready-to-use financial modeling template with data for the S&P, cryptos, and Apple/Google stocks, saving chart formatting so you focus on probability and the method of moments.

Learn to compute discrete probability densities for S&P 500 log returns from historical data, convert densities to percentage probabilities, and interpret the cumulative density function and pdf versus distribution.

Clarifies population versus sample in financial time series and presents mu, sigma, x-bar, s, variance, and standard deviation for inferring population parameters.

Explain the second central moment as variance (sigma squared), show population and sample variance formulas using deviations from the mean, and justify the t minus one adjustment.

Explore the standard normal distribution and its density function, standardize data to zero mean and unit variance, and use the area under the curve to assess probabilities.

Learn to build and analyze a normal distribution from scratch in Excel, using density and cumulative distribution functions, standard normal concepts, and a probability integral transform.

Practice skewness and kurtosis from sample data in Excel using mean, standard deviation, and z-scores; apply skew and kurtosis functions and note excess kurtosis.

Compare the empirical CDF and PDF of financial returns with the normal and Student t densities, highlighting how the Student t better fits tail risk and real data.

Compare the empirical pdf of standardized returns with the normal pdf and the student t pdf, overlay the curves, and discuss scaling, degrees of freedom, and verification.

Learn to compute an empirical cumulative distribution function (ECDF) from sorted returns, adjust for ties, and compare it to the normal CDF to reveal leptokurtic tails and nonlinearity.

Learn how to use a q-q plot to compare empirical data to a normal distribution by plotting quantiles, handling boundary issues, and interpreting deviations in tails.

Explore the meanings of the pdf and cdf, their parameters mu and sigma, and how to read left-hand side notation, area integrals, and inverse cdf in normal distributions.

Explore covariance and Pearson's correlation coefficient to understand how Bitcoin and Ethereum move together in time series, using variances, standard deviations, joint distributions, and copulas.

Explore how copulas link different marginal distributions to a joint distribution using Sklar's theorem, focusing on Gaussian, Student-t, and empirical copulas for risk and arbitrage.

Model the dependency between two assets with a gaussian copula, converting log returns to uniform marginals and applying inverse standard normal transforms. Explore conditional probabilities and model selection.

Compute the Gaussian copula conditional probability of one asset’s return given another’s, using the standard normal distribution and rho, with Bitcoin and Ethereum illustrating statistical arbitrage.

Explore how financial econometrics uses linear regression to model asset relationships in time series, estimate parameters with ordinary least squares or maximum likelihood, and test hypotheses with statistical tests.

Explore simple ordinary least squares with ANOVA concepts, deriving alpha and beta, calculating residuals, SSR, SSE, RSS, and R-squared, and assessing statistical significance with standard errors.

Test hypotheses in simple linear regression for time series analysis using t statistics, null hypothesis that beta equals zero, and a two-tailed approach with degrees of freedom and p-values.

Execute a simple ordinary least squares regression, compute t statistics for alpha and beta with the residuals' degrees of freedom, assess significance with an f statistic and p-values using linest.

Explore multiple OLS as an extension of simple regression, using lagged predictors with an X matrix; learn transpose, dot product, inverse, and Excel linest for coefficients and standard errors.

Estimate a multiple OLS model for S&P 500 returns using Nasdaq, Apple, Google, and a constant; verify coefficients with matrix algebra, standard errors, and significance tests.

Explore maximum likelihood estimation using a normal density in Excel, computing the pdf, log probabilities, and joint probability under independence, then optimize mu and variance via gradient descent.

Build and maximize the log-likelihood for a linear regression with normal density. Compare homoscedastic assumptions and MLE versus OLS, then note variance modeling with GARCH.

Estimate an ma1 model with maximum likelihood, solving for alpha, phi, and variance using starting values and Excel solver. See how crypto returns XC, USDt respond to prior shocks.

Understand autoregressive and moving average components in arma models, including ar(p) and ma(q) with corresponding phi and theta coefficients. Learn to estimate arma(p,q) in excel with ar1, ma1 examples.

Explore AR1 vs MA1 adaptation in ARMA, compare OLS and maximum likelihood estimation, and show AR1 OLS matching MLE results for phi and constant using log-likelihood.

learn to perform full ARMA estimation with maximum likelihood, estimate AR (phi) and MA (theta) parameters, compute x hat and epsilon, and compare resulting fits.

Explore the Gauss-Markov theorem and why ordinary least squares is the blue, best linear unbiased estimator under linearity, random sampling, no multicollinearity, zero conditional means, and homoscedasticity.

Explore the partial autocorrelation function as a diagnostic tool to isolate each lag's contribution in autoregressive models and compare with ACF, guiding PACF-informed AR order amid multicollinearity.

Explore how to convert prices into stationary returns for XECUSDT and compute the autocorrelation function across lags one to three, including a note on log returns and potential trading signals.

Explore the autocorrelation function for XECUSDT in time series analysis, using up and down day states to infer transitions and test a short-sell approach with prior positive returns.

Learn how weak stationarity, with a constant mean, variance, and autocovariance, underpins integration and cointegration, and how differencing or returns help avoid spurious regressions in financial time series.

Identify unit roots to assess stationarity by ensuring roots lie within the unit circle. Explore i(0) versus i(1) and how differencing and the augmented dickey-fuller test relate to ar models.

Apply the Dickey-Fuller and augmented Dickey-Fuller tests to assess stationarity in time series, using delta y, y lag, and optional trend or constant, and interpret t-stats against critical values.

Explore cointegration and mean reversion by testing integration, constructing the stationary spread from residuals of a linear regression, and applying Engle-Granger two-step and error correction models for pairs trading.

Explore the error correction model, cointegration, and residuals, measuring the speed of adjustment (gamma) and mean reversion in changes of x and y with lagged effects.

Explore how volatility, as a derived variance, varies over time with conditional heteroskedasticity. Learn the symmetrical GARCH model, its autoregressive structure, and how maximum likelihood estimation captures volatility dynamics.

Explore garch (symmetrical) volatility modelling using Bitcoin and Ethereum daily prices, estimating conditional variance with mean-corrected returns and maximum likelihood, and compare annualized volatility between assets.

Construct an agarch model by including gamma and estimating via maximum likelihood with a solver; interpret positive gamma as greater volatility reaction to negative shocks, with annualized volatility around 94.2%.

Congratulate students on finishing the course and guide essential reading for financial time series topics like cointegration, copulas, and GARCH, with books by Brooks, Tse, and Alexander.

Explore granger causality in time series, noting that one asset tends to precede yet not cause changes, with lag selection, p-values, and mean-reverting spread concepts like Ornstein-Uhlenbeck.