Let rt denote the residual which is represented byrt=yt?N^t.(14)The residual represents linear components that cannot be modeled by SVR model. The SVR and ARIMA parameters are estimated by applying PSO, as described previously. Forecasting results from SVR and ARIMA models will be combined to represent the forecasting www.selleckchem.com/products/Bicalutamide(Casodex).html results of the proposed hybrid model. The combined forecast is shown by the formula (15)y^t=N^t+L^t.(15)Figure 1 shows the flowchart for the proposed hybrid model, PSOSVR_PSOARIMA. Figure 1The Flow chart for the proposed hybrid PSOSVR and PSOARIMA model.4. Data Set and Model EvaluationThis section describes the data set used and the model evaluation carried out in this study.4.1.

Data SetThis study uses annual data of property crime rates, consumer price index for all urban consumers (Apparel), gross domestic product in United States natural log of billions of chained 2005 US Dollars, and unemployment rate (20 to 24 years) from 1960 to 2009 in United States. The crime rates are obtained from the Uniform Crime Reporting Statistics website (http://www.ucrdatatool.gov/), while economic indicators data are available on Economic Research Federal Reserve Bank of St. Louis website (http://research.stlouisfed.org/). Property crime data comprised property crime rate, vehicle rate, larceny-theft rate, and burglary rate. In addition to economic indicators, two crime indicators are also used in the model, which are one-year lagged property crime rate (PCR) and one-year lagged robbery rate. Data is divided into training and test data sets.

The training data set is used to develop the models while the test data set is used to evaluate the forecasting performance of the models. In this study, 90 percent of the data will be used as training (1961 to 2004) and 10 percent is as test data set (2005 to 2009). 4.2. Model EvaluationThe performance of the proposed hybrid model is evaluated using the test data set. The forecasting performance of the proposed hybrid model is evaluated using four types of evaluations.(i) Descriptive Statistics. Graph of actual values and forecasting of testing data set is plotted in order to see the pattern of model predictions compared with the actual data patterns. A box plot diagram is used to check the error values. Box plot is used to see the dispersion of error values such as the position of median whether it is close to zero, and to ensure that there are no extreme values in error.

(ii) Quantitative Error Measurements. Four types of quantitative error measurements are conducted, namely, root mean square error (RMSE), mean square error (MSE), mean absolute percentage error (MAPE), and mean absolute deviation (MAD). Formulas (16), (17), (18), and (19) are the equation Entinostat for RMSE, MSE, MAPE, and MAD, respectively.