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Simulation Methods

5 important questions on Simulation Methods

Why do we use simulation methods?

Some questions are unable to answer given the amount of data, or just unobservable data. Or just because of their complexity, due to behaviour of series and inter-relationships between them. Or just fat tails, strucutural breaks or bi-directional causality which makes inference less reliable (messy data).

Simulation help to behave like real scientist, conducting experimetns under controlled conditions. It offers complete flexibility and can mimic a functioning system as it evolves. Particularly useful wel models are very complex or sample data is small.

What about Monte Carlo simulation?

Used to investigate the properties and behaviour of various statistics of interest. Might be useful in situations like:
- Simultaneous equation bias (treating endogenous as exogenous)
- Dickey-Fuller appropriate test
- Effect of heteroskedasticity to size and power of a test for autocorrelation
- Exotic options
- Macroeconomic changes
- Stress testing

First, specify the model and the data generating process, with corresponding probability distribution. Second, perform regression and calculate test statistic.
Third, save the test statistic. Four, repeat N times. Asymptotic arguments apply in MC.

When will bootstrapping be ineffective?

- Outliers in the data can affect the results, primarily depends how often they are sampled
- Non-independent data, implying no autcorrelation. To solve, moving block bootstrap can be done, by sampling whole blocks.
Note: variance reduction techniques can be used as well

What about random number generation?

Uniform (0,1) distribution, equal chance of being selected. But it needs a base, like Y(0) is the seed, the initial value of y. But the first Ys will be affected by this, therefore sample more than needed and leave first part out. Sort of pseudo-random numbers (deterministic). Eventually it will start to repeat. Uniform draws can be transformed to other distributions.

What are disadvantages of simulation approach?

- It might be computationally expensive, although fast CPU the complexity accelarates as well
- Results might not be precise (unrealistic assumptions, like ignoring fat-tails)
- The results might be hard to replicate (specific to the given investigation)
- Simulation results are experiment-specific, only applies to that experiment.
It can be dangerous in the wrong hands (as many other tools)

The question on the page originate from the summary of the following study material:

Part 2: Quantitative Analysis

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