This chapter provides an overview of solution and estimation techniques for dynamic stochastic general equilibrium models. We cover the foundations of numerical approximation techniques as well as statistical inference and survey the latest developments in the field.

Vector autoregressive moving-average (VARMA) processes are suitable models for producing linear forecasts of sets of time series variables. They provide parsimonious representations of linear data generation processes. The setup for these processes in the presence of stationary and cointegrated...

There are simple well-known conditions for the validity of regression and correlation as statistical tools. We analyse by examples the effect of nonstationarity on inference using these methods and compare them to model based inference using the cointegrated vector autoregressive model. Finally...

We analyze the properties of various methods for bias-correcting parameter estimates in both stationary and non-stationary vector autoregressive models. First, we show that two analytical bias formulas from the existing literature are in fact identical. Next, based on a detailed simulation...

Vector autoregressions with Markov-switching parameters (MS-VARs) fit the data better than do their constant-parameter predecessors. However, Bayesian inference for MS-VARs with existing algorithms remains challenging. For our first contribution, we show that Sequential Monte Carlo (SMC)...

We conduct a simulation study of Local Projection (LP) and Vector Autoregression (VAR) estimators of structural impulse responses across thousands of data generating processes, designed to mimic the properties of the universe of U.S. macroeconomic data. Our analysis considers various...