Main goal of the new research will be trying to predict movement of money, capital, derivative and fx market within the monetary, real and fiscal economy sector movements.
In the first phase, I'll be creating a network based on FED data on US economy, on the next phase EUROZONE based on ECB data and on the last phase Azia based on China and Japan central banks.
The final step will be interconnecting those 4 strategic points of worlds economy and try to learn economic bonds between them. Every phase of my research will be posted online.
Saturday, November 3, 2007
Sunday, October 21, 2007
Conclusion
The focus of this research was in finding an effective model for predicting US federal funds target rate using neural networks . Macroeconomic data represented with fifteen input variables were used as the input, while the output was the federal funds target rate. Three NN algorithms were tested including multilayer perceptron, radial basis, and generalized regression resulting with three different NN models. Individual model results show that the radial basis neural network outperforms other models in the sense of the generalization error. The average error obtained by a 10-fold cross validation procedure showed that the radial basis function network has the smallest average mean RMSE of all three models. The selection of input variables in the best model shows that the most important predictors of the federal funds target rate are discount rate, 3-month treasury rate, 10-year treasury rate, oil price, and production price index .
As guidelines for futher research, we suggest to test time-seria models with lags and multiple time-horizons (1-month, 3-months, and 6-months ahead) using radial basis and recurrent neural networks, to evaluate generalization ability using more samples, and to test the methodology on more datasets from other countries in order to compare the importance of predictor variables accross coutries.
As guidelines for futher research, we suggest to test time-seria models with lags and multiple time-horizons (1-month, 3-months, and 6-months ahead) using radial basis and recurrent neural networks, to evaluate generalization ability using more samples, and to test the methodology on more datasets from other countries in order to compare the importance of predictor variables accross coutries.
Results
Three different neural network algoritms were used, each of them was tested in a 10-fold cross-validation procedure in order to estimate the generalization error of the model. Both mean square error (MSE) and root mean square error (RMSE) were computed while the RMSE was used as the evaluation instrument. The results are presented in Tables 2, 3, and 4.
It can be seen from Table 2 that the average MSE of 10 MLP neural networks tested in the cross validation resampling procedure was 0.009879, while the average RMSE was 0.089345. As suggested by [9], the average RMSE of all 10 networks is used as the population error. The test result obtained on the whole train sample (450 cases) is reffered as the apparent error. As presented in Table 2, the apparent error of the tested MLP network is 0.289761. The excess error of the MLP network, computed as the difference among the population error and the apparent error [9] was - 0.200416. Since the average RMSE obtained on the test sample in the cross validation resampling procedure contains a bias due to the selected size of the network, the final validation of the network models is conducted on the hold-out test sample. The average RMSE obtained on the hold-out sample was 0.216812. The topology of the NN that produced the best out-of-sample performance consisted of 5 input units, 6 hidden units, and 1 output. The dimension of hidden units was reduced by pruning, while the number of input variables was reduced by the sensitivity analysis. Selected input variables were: 3-month treasury (3MT), industrial production index (IPI), inflation rate (INFL), consumer price index (CPI), and S&P500 index (SP500). Table 3 presents the results of the RBF network tested in the cross validation resampling procedure.
The average MSE of all ten RBF networks was 0.006445, while the average RMSE was 0.075413. The apparent error was 0.08979, resulting with the excess error of -0.014376. RBF network that produced the best out-of-sample RMSE consisted of 5 input units, 15 hidden and 1 output unit. Selected input variables were: discount rate (Disc), 3-month treasury rate (3MT), 10-year treasury rate (10YT), oil price (OIL), and production price index (PPI). The results of the GRNN tested in the cross validation resampling procedure are presented in Table 4.
The average MSE of all ten GRN networks was 0.008004, while the average RMSE was 0.085957. The apparent error was 0.070212, resulting with the excess error of 0.015745. GRNN that produced the best out-of-sample RMSE consisted of 15 input units, 270 units in the hidden, 2 hidden units in the summation/division layer, and 1 output unit. All fifteen input variables were selected as important for the GRNN model.
It is evident that the RBFN model produced the lowest generalization error (average cross-validation RMSE and average out-of-sample RMSE (0.053904)). It is surprising that the average cross-validation (i.e. population) errors of the RBFN and MLP networks are lower than their apparent errors, therefore producing negative excess errors. It is the opposite with the GRNN network, which gives higher average cross-validation RMS error than the apparent error.
When the influence of the input variables to the model is concerned, each of the three best NN models extracted different set of important predictors. MLP and RBFN both extracted only five input variables as important to the model, while the GRNN did not reduce its input space.
It can be seen from Table 2 that the average MSE of 10 MLP neural networks tested in the cross validation resampling procedure was 0.009879, while the average RMSE was 0.089345. As suggested by [9], the average RMSE of all 10 networks is used as the population error. The test result obtained on the whole train sample (450 cases) is reffered as the apparent error. As presented in Table 2, the apparent error of the tested MLP network is 0.289761. The excess error of the MLP network, computed as the difference among the population error and the apparent error [9] was - 0.200416. Since the average RMSE obtained on the test sample in the cross validation resampling procedure contains a bias due to the selected size of the network, the final validation of the network models is conducted on the hold-out test sample. The average RMSE obtained on the hold-out sample was 0.216812. The topology of the NN that produced the best out-of-sample performance consisted of 5 input units, 6 hidden units, and 1 output. The dimension of hidden units was reduced by pruning, while the number of input variables was reduced by the sensitivity analysis. Selected input variables were: 3-month treasury (3MT), industrial production index (IPI), inflation rate (INFL), consumer price index (CPI), and S&P500 index (SP500). Table 3 presents the results of the RBF network tested in the cross validation resampling procedure.
The average MSE of all ten RBF networks was 0.006445, while the average RMSE was 0.075413. The apparent error was 0.08979, resulting with the excess error of -0.014376. RBF network that produced the best out-of-sample RMSE consisted of 5 input units, 15 hidden and 1 output unit. Selected input variables were: discount rate (Disc), 3-month treasury rate (3MT), 10-year treasury rate (10YT), oil price (OIL), and production price index (PPI). The results of the GRNN tested in the cross validation resampling procedure are presented in Table 4.
The average MSE of all ten GRN networks was 0.008004, while the average RMSE was 0.085957. The apparent error was 0.070212, resulting with the excess error of 0.015745. GRNN that produced the best out-of-sample RMSE consisted of 15 input units, 270 units in the hidden, 2 hidden units in the summation/division layer, and 1 output unit. All fifteen input variables were selected as important for the GRNN model.
It is evident that the RBFN model produced the lowest generalization error (average cross-validation RMSE and average out-of-sample RMSE (0.053904)). It is surprising that the average cross-validation (i.e. population) errors of the RBFN and MLP networks are lower than their apparent errors, therefore producing negative excess errors. It is the opposite with the GRNN network, which gives higher average cross-validation RMS error than the apparent error.
When the influence of the input variables to the model is concerned, each of the three best NN models extracted different set of important predictors. MLP and RBFN both extracted only five input variables as important to the model, while the GRNN did not reduce its input space.
Descriptive statistics
The in-sample data consisted of 440 cases (80% of the whole sample), while the rest of 20% of the data were used as the hold-out sample (111 cases). For the purpose of the 10-fold cross validation the in-sample data were divided into 10 equally sized independent samples, each of them consisted of 44 cases, and NN models were cross validated following the procedure described in previous section. Each training subsample consisted of 396 training cases, furtherly splitted into two subsamples (264 cases for training the network and 132 cases for early stopping, and optimizing the network topology). The experiments were conducted using Statistica Neural Network software.
Wednesday, September 26, 2007
Data inputs
The total dataset consists of 551 monthly observations covering the period from January 1959 to December 2005, available from the Federal Reserve's economic and financial database (FRED) described in [15].
The choice of input variables was made on the basis of some previous research suggesstions ([11],[13]). Fifteen input variables describing US capital market and macroeconomic situation are used to predict the value of the the US federal funds target rate in the next month (FFR). They can be grouped into several categories as follows: (1) capital market indicators: S&P500 index (S&P500), Dow Jones Industrial Average (DJI); (2) inflation indicators: consumer price index (CPI), inflation rate (INFL), US unemployment rate (UNEMPLOY), producer price index (PPI); (3) Economic real sector indicators: industrial production index (IPI), personal consumption expenditures (PCE), housing starts (HOUSING); (4) financial market indicators: discount rate (DISC_RATE), 10 year treasury rate (10Y_TREASURY), 3 month treasury bill rate (3M_TREASURY); (5) monetary aggregates: money supply (M1); and (6) commodities market indicators: gold price (GOLD), oil price (OIL).
In order to eliminate the trend influence and amplitude influence, data were transformed into percentage change and normalized before entering neural network models. Descriptive statistics
The choice of input variables was made on the basis of some previous research suggesstions ([11],[13]). Fifteen input variables describing US capital market and macroeconomic situation are used to predict the value of the the US federal funds target rate in the next month (FFR). They can be grouped into several categories as follows: (1) capital market indicators: S&P500 index (S&P500), Dow Jones Industrial Average (DJI); (2) inflation indicators: consumer price index (CPI), inflation rate (INFL), US unemployment rate (UNEMPLOY), producer price index (PPI); (3) Economic real sector indicators: industrial production index (IPI), personal consumption expenditures (PCE), housing starts (HOUSING); (4) financial market indicators: discount rate (DISC_RATE), 10 year treasury rate (10Y_TREASURY), 3 month treasury bill rate (3M_TREASURY); (5) monetary aggregates: money supply (M1); and (6) commodities market indicators: gold price (GOLD), oil price (OIL).
In order to eliminate the trend influence and amplitude influence, data were transformed into percentage change and normalized before entering neural network models. Descriptive statistics
Modeling federal funds target rate using neural networks
The paper aims to find an effective model for predicting US federal funds target rate using neural networks. The model is based on macroeconomic data with fifteen input variables, while the output was the federal funds target rate, used by The Federal Reserve bank to control the monetary stability in the country. Different neural network architectures were tested using multilayer perceptron, radial basis, and generalized regression algorithms. The best neural network model is selected on the basis of generalization ability. Generalization error of all models is examined using 10-fold cross validation resempling. The results show that neural networks are able to incorporate the relationship among input variables with a high accuracy. The created model revealed that artificial intelligence methods have great potential in the area of interest rate predictions and could be used for future research in that area.
Federal funds rate (FFR) is an interest rate determined by the Federal reserve bank (Fed) and used for over-night loans conducted among banks in order to ensure the bank liquidity and enhance its efficiency. It is also used as a baseline for determining other interest rates (short-term and long-term treasury loans, short-term and long-term credits, and mortgage loans. The importance of predicting the federal funds target rate is emphasized by the research of Lobo [8], who found that "target change announcements convey new information to the stock market." According to [8], announcements of a joint target and discount rate change especially influence the risk aversion and the market volatility. Most of the research in financial modeling was focused on parametric methods, while nonparametric methods, such as neural neural networks (NNs) were not investigated enough.
The paper is focused on finding an effective model for predicting the US federal funds target rate using NNs. The dataset covered the period from January 1959 to December 2005. Three NN algorithms were tested: multilayer perceptron, radial basis function network, and general regression network. The best model selection is based on the generalization error, which was estimated by a 10-fold cross-validation procedure.
The rest of the paper describes previous research results, NN methodology used, data, modeling procedure including sampling and cross validation, followed by the results and conclusion.
Federal funds rate (FFR) is an interest rate determined by the Federal reserve bank (Fed) and used for over-night loans conducted among banks in order to ensure the bank liquidity and enhance its efficiency. It is also used as a baseline for determining other interest rates (short-term and long-term treasury loans, short-term and long-term credits, and mortgage loans. The importance of predicting the federal funds target rate is emphasized by the research of Lobo [8], who found that "target change announcements convey new information to the stock market." According to [8], announcements of a joint target and discount rate change especially influence the risk aversion and the market volatility. Most of the research in financial modeling was focused on parametric methods, while nonparametric methods, such as neural neural networks (NNs) were not investigated enough.
The paper is focused on finding an effective model for predicting the US federal funds target rate using NNs. The dataset covered the period from January 1959 to December 2005. Three NN algorithms were tested: multilayer perceptron, radial basis function network, and general regression network. The best model selection is based on the generalization error, which was estimated by a 10-fold cross-validation procedure.
The rest of the paper describes previous research results, NN methodology used, data, modeling procedure including sampling and cross validation, followed by the results and conclusion.
Subscribe to:
Posts (Atom)
