- By Admin
- December 31, 2014
- Comments Off on Overview of Different Types of Forecasting Techniques
Here is a quick review of each methodology and several quick getting started examples in using the software. More detailed descriptions and example models of each of these techniques are found in Risk Simulator.
ARIMA. Autoregressive integrated moving average (ARIMA, also known as Box– Jenkins ARIMA) is an advanced econometric modeling technique. ARIMA looks at historical time-series data and performs back-fitting optimization routines to account for historical autocorrelation (the relationship of one value versus another in time) and accounts for the stability of the data to correct for the nonstationary characteristics of the data. This predictive model learns over time by correcting its forecasting errors. Advanced knowledge in econometrics is typically required to build good predictive models using this approach.
Auto ARIMA. The Auto-ARIMA module automates some of the traditional ARIMA modeling by automatically testing multiple permutations of model specifications and returning the best-fitting model. Running the Auto-ARIMA module is similar to running regular ARIMA forecasts. The differences being that the P, D, Q inputs are no longer required and that different combinations of these inputs are automatically run and compared.
Basic Econometrics. Econometrics refers to a branch of business analytics, modeling, and forecasting techniques for modeling or forecasting the behavior of, certain business, economic, finance, physics, manufacturing, operations, and any other variables. Running the Basic Econometrics models is similar to regular regression analysis except that the dependent and independent variables are allowed to be modified before a regression is run.
Basic Auto Econometrics. This methodology is similar to basic econometrics, but thousands of linear, nonlinear, interacting, lagged, and mixed variables are automatically run on your data to determine the best-fitting econometric model that describes the behavior of the dependent variable. It is useful for modeling the effects of the variables and for forecasting future outcomes, while not requiring the analyst to be an expert econometrician.
Custom Distributions. Using Risk Simulator, expert opinions can be collected and a customized distribution can be generated. This forecasting technique comes in handy when the dataset is small or the goodness-of-fit is bad when applied to a distributional fitting routine.
GARCH. The generalized autoregressive conditional heteroskedasticity (GARCH) model is used to model historical and forecast future volatility levels of a marketable security (e.g., stock prices, commodity prices, oil prices, etc.). The dataset has to be a time series of raw price levels. GARCH will first convert the prices into relative returns and then run an internal optimization to fit the historical data to a mean-reverting volatility term structure, while assuming that the volatility is heteroskedastic in nature (changes over time according to some econometric characteristics). Several variations of this methodology are available in Risk Simulator, including EGARCH, EGARCH-T, GARCH-M, GJR-GARCH, GJR-GARCH-T, IGARCH, and T-GARCH.
J-Curve. The J-curve, or exponential growth curve, is one where the growth of the next period depends on the current period’s level and the increase is exponential. This phenomenon means that over time, the values will increase significantly from one period to another. This model is typically used in forecasting biological growth and chemical reactions over time.
Markov Chains. A Markov chain exists when the probability of a future state depends on a previous state and when these periods are linked together, a chain is formed that reverts to a long-run steady state level. This approach is typically used to forecast the market share of two competitors. The required inputs are the starting probability of a customer in the first store (the first state) returning to the same store in the next period versus the probability of switching to a competitor’s store in the next state.
Maximum Likelihood on Logit, Probit, and Tobit. Maximum likelihood estimation (MLE) is used to forecast the probability of something occurring given some independent variables. For instance, MLE is used to predict if a credit line or debt will default given the obligor’s characteristics (30 years old, single, salary of $100,000 per year, and total credit card debt of $10,000), or the probability a patient will have lung cancer if the person is a male between the ages of 50 and 60, smokes five packs of cigarettes per month or year, and so forth. In these circumstances, the dependent variable is limited (i.e., limited to being binary 1 and 0 for default/die and no default/live, or limited to integer values such as 1, 2, 3, etc.), and the desired outcome of the model is to predict the probability of an event occurring. Traditional regression analysis will not work in these situations (the predicted probability is usually less than zero or greater than one, and many of the required regression assumptions are violated, such as independence and normality of the errors, and the errors will be fairly large).
Multivariate Regression. Multivariate regression is used to model the relationship structure and characteristics of a certain dependent variable as it depends on other independent exogenous variables. Using the modeled relationship, we can forecast the future values of the dependent variable. The accuracy and goodness-of-fit for this model can also be determined. Linear and nonlinear models can be fitted in the multiple regression analysis.
Nonlinear Extrapolation. In this methodology, the underlying structure of the data to be forecasted is assumed to be nonlinear over time. For instance, a dataset such as 1, 4, 9, 16, 25 is considered to be nonlinear (these data points are from a squared function).
S-Curves. The S-curve, or logistic growth curve, starts off like a J-curve, with exponential growth rates. Over time, the environment becomes saturated (e.g., market saturation, competition, overcrowding), the growth slows, and the forecast value eventually ends up at a saturation or maximum level. The S-curve model is typically used in forecasting market share or sales growth of a new product from market introduction until maturity and decline, population dynamics, or some other naturally occurring phenomenon.
Spline Curves. Sometimes there are missing values in a time-series dataset. For instance, interest rates for years 1 to 3 may exist, followed by years 5 to 8, and then year 10. Spline curves can be used to interpolate the missing years’ interest rate values based on the data that exist. Spline curves can also be used to forecast or extrapolate values of future time periods beyond the time period of available data. The data can be linear or nonlinear.
Stochastic Process Forecasting. Sometimes variables cannot be readily predicted using traditional means; these variables are said to be stochastic. Nonetheless, most financial, economic, and naturally occurring phenomena (e.g., motion of molecules through the air) follow a known mathematical law or relationship. Although the resulting values are uncertain, the underlying mathematical structure is known and can be simulated using Monte Carlo risk simulation. The processes supported in Risk Simulator include Brownian motion random walk, mean-reversion, jump-diffusion, and mixed processes, useful for forecasting nonstationary time-series variables.
Time-Series Analysis and Decomposition. In well-behaved time-series data (typical examples include sales revenues and cost structures of large corporations), the values tend to have up to three elements: a base value, trend, and seasonality. Time-series analysis uses these historical data and decomposes them into these three elements, and recomposes them into future forecasts. In other words, this forecasting method, like some of the others described, first performs a backfitting (backcast) of historical data before it provides estimates of future values (forecasts).
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