A Very Short Course on Time Series Analysis
1
Introduction
2
The Structure of Temporal Data
2.1
Example: Air Pollution and Health
2.2
Fixed vs. Random Variation
2.3
Goals of Time Series Analysis
2.3.1
Forecasting
2.3.2
Filtering
2.3.3
Time Scale Analysis
2.3.4
Regression Modeling
2.3.5
Smoothing
2.4
Example: Particulate Matter Concentrations
2.5
Trend-Season-Residual Decomposition
2.6
Example: Filtering an Endowment Spending Rule
2.7
Stationarity
2.8
Autocorrelation
2.9
Gaussian Processes
3
Frequency and Time Scale Analysis
3.1
The Nyquist Frequency
3.2
Just a Bunch of Sines and Cosines
3.3
Partitioning the Variation
3.4
Spectral Analysis
3.4.1
Smoothing the Periodogram
3.5
The Fourier Transform
3.5.1
Example
3.6
The Fast Fourier Transform (FFT)
3.6.1
Example: A Simple FFT
3.6.2
The Cooley-Tukey Algorithm
4
Time Series Regression Modeling
4.1
Objectives
4.2
Filtering Time Series
4.2.1
Fourier Transforms of Convolutions
4.2.2
Low-Pass Filter
4.2.3
High-Pass Filter
4.2.4
Matching Filter
4.2.5
Exponential Smoother
4.3
Distributed Lag Models
4.3.1
Example: Baltimore Temperature and Mortality
4.4
Temporal Confounding
4.4.1
Bias from Omitted Temporal Confounders
4.4.2
Example: Confounding by Smoothly Varying Factors
4.5
Residual Autocorrelation
5
State Space Models and the Kalman Filter
5.1
Example: A Simple Spacecraft
5.2
The Kalman Filter
5.3
Deriving the One-dimensional Case
5.4
General Kalman Filter
5.5
Missing Data
5.6
Example: Filtering the Rotation Angle of a Phone
5.7
Example: Tracking the Position of a Car
5.8
Example: Estimating the Apogee of a (Model) Rocket
5.9
Exponential Smoothing
5.10
Complementary Filter
6
Maximum Likelihood Estimation
6.1
Example: An
\(AR(1)\)
Model
6.2
Maximum Likelihood with the Kalman Filter
6.3
Example: A Local Level Model
6.4
Example: An
\(AR(2)\)
Model
7
Point Process Analysis
7.1
Stationary Poisson Process
7.1.1
Connection to Survival Analysis
7.1.2
Connection to Time Series Analysis
7.1.3
Example: Southern California Earthquakes
7.2
Conditional Intensities
7.3
Conditional Intensity Models
7.3.1
Cluster Models
7.3.2
ETAS Model
7.3.3
Self-Correcting Models
7.4
Estimation
7.5
Residual Analysis
7.6
Simulation and Prediction
Published with bookdown
A Very Short Course on Time Series Analysis
5.10
Complementary Filter
