Solving ARMA model – minimization of squared error
Key focus: Can a unique solution exists when solving ARMA (Auto Regressive Moving Average) model ? Apply minimization of squared error to find out. As discussed in the previous post, the ARMA model is...
View ArticleYule Walker Estimation and simulation in Matlab
If a time series data is assumed to be following an Auto-Regressive (AR(N)) model of given form, the natural tendency is to estimate the model parameters a1,a2,…,aN. Least squares method can be applied...
View ArticleAutoCorrelation (Correlogram) and persistence – Time series analysis
The agenda for the subsequent series of articles is to introduce the idea of autocorrelation, AutoCorrelation Function (ACF), Partial AutoCorrelation Function (PACF) , using ACF and PACF in system...
View ArticleLinear Models – Least Squares Estimator (LSE)
Key focus: Understand step by step, the least squares estimator for parameter estimation. Hands-on example to fit a curve using least squares estimation Background: The various estimation...
View ArticleBLUE estimator
Why BLUE : We have discussed Minimum Variance Unbiased Estimator (MVUE) in one of the previous articles. Following points should be considered when applying MVUE to an estimation problem MVUE is the...
View ArticleGenerate correlated Gaussian sequence (colored noise)
Key focus: Colored noise sequence (a.k.a correlated Gaussian sequence), is a non-white random sequence, with non-constant power spectral density across frequencies. Introduction Speaking of Gaussian...
View ArticleGenerating colored noise with Jakes PSD: Spectral factorization
The aim of this article is to demonstrate the application of spectral factorization method in generating colored noise having Jakes power spectral density. Before continuing, I urge the reader to go...
View ArticleGenerate color noise using Auto-Regressive (AR) model
Key focus: Learn how to generate color noise using auto regressive (AR) model. Apply Yule Walker equations for generating power law noises: pink noise, Brownian noise. Auto-Regressive (AR) model An...
View ArticleMarkov Chains – Simplified !!
Key focus: Markov chains are a probabilistic models that describe a sequence of observations whose occurrence are statistically dependent only on the previous ones. ● Time-series data like speech,...
View ArticleHidden Markov Models (HMM) – Simplified !!!
Markov chains are useful in computing the probability of events that are observable. However, in many real world applications, the events that we are interested in are usually hidden, that is we don’t...
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