Predicting UK Short-Term Monthly Rates Using Unemployment Rate, GDP Growth Rate, and Inflation Rate - Research Paper Example

Predicting UK short term monthly rates using Unemployment rate, GDP Growth Rate and Inflation Rate Contents Abstract……………………………………………………………………3 Background…………………………………………………………………4 Aims and Objectives………………………………………………………6 Methodology…………………………………………………………………7 Results………………………………………………………………………..8 Discussion & Conclusion…………………………………………………..32 Reference……………………………………………………………………..37 Appendix-1………………………………………………………………….39 Abstract The variables like Unemployment rate, GDP Growth Rate, Inflation Rate are important considerations for a country to decide upon its short term interest rates and on a wider spectrum the monetary policy. This study was aimed to predict the short term interest rates based on the GDP growth rate, inflation rate and the unemployment rate in the United Kingdom. The study also reflected upon the forecasts and the predictions of the short term interest rates in the future based on the GDP growth rate, inflation rate and the unemployment rates. It was observed that short term interest rates in UK will decrease whenever the unemployment rates will rise and will increase with inflation and it will decrease with increased GDP but the correlation was not statistically significant. This prediction of the above was confirmed both by the OLS formed together with all variables and individually regressing each GDP growth rate , inflation rate and unemployment rate on short term interest rates. The ARMA model describes the system as a function of the unobserved shocks which means the short term interest rates may be shocked by fundamental information and exhibits reversion effects due to the market variants. Even after making assumptions for the phi and theta components the regression equation was similar to the basic regression equation where it was once again reflected that whenever unemployment rates will increase the short term interest rates has a trend to decrease and whenever shot term interest rates will increase inflation will increase. Hence the reproducibility of the uniform model through the ordinary least squares regression, AR model, ARMAX model justified the validity of the model and is a good one in predicting future values of short term interest rates based on inflation rates and unemployment rates. Background The variables like Unemployment rate, GDP Growth Rate, Inflation Rate are important considerations for a country to decide upon its short term interest rates and on a wider spectrum the monetary policy. This policy is dependant on the rates of interest in an economy, which means this determines the price at which the money might be borrowed and determines the total supply of money. Monetary policy influences various components like economic growth (GDP growth rate), inflation, the exchange rates with other currencies and the unemployment status of a country (Corsetti, 2005). If the currency is monopolized, and the monetary authorities are under the control of central bank then this authority can alter the money supply and hence influence the interest rates. The monetary policy is jeopardized if the rates of interest are high and the supply of money in the market decreases. While the policy is referred to as expansionary when the interest rates are reduced and the money supply to the market increases. The interest rates devised by the banks can be intended to create economic growth of a country and it is called accommodative, it is referred to as neutral when the interest rates neither create growth or tackles inflation and finally the rate is considered tight when it is used to reduce inflation (Corsetti, 2011). Thus it can be viewed that monetary policy is the process by which the government of the country, the monetary authority or centralized banks of a country controls the flow and availability of money and at the same time the cost of money or the rate of interest designed to achieve a set of objectives oriented to increase the growth and foster the stability of economy of a country (Devereux, 2003). Thus the interest rates and the monetary policy are important attributes for the policy makers to take credible decisions. If the private companies believe that the policy makers are aiming to reduce the inflation then they will anticipate lowering of prices for their commodities or services in the future and rationalize their profitable expectations. Similarly if an employee feels that the policy makers are not working on the process of reducing inflation then they will have to negotiate with the interviewers or superiors on wages that will help them to meet their financial expectations in the future. In fact with the higher wages there will be a increase in the consumers demand which is called demand pull inflation and at the same time it will increase a company’s costs referred to as cost push inflation. Under this scenario the private companies will anticipate a higher inflation and the inflation rises (Clarida et al, 2002). The private agents are aware of the fact that if they anticipate low inflation, the policy implemented would be of expansionist type and hence the private agents expect a high inflation, Hence the credible decisions must be announced in a tangible fashion (Corsetti, 2011). GDP refers to the market value of the total accepted and recognized final commodities produced within a given period of time. It represents the sum of investments, government spending, net exports and the consumption. Consumption which is the largest component of GDP includes the private or household consumption expenditure. The investments refer to the expenditure made by the industries on equipment and manpower. The spending of the Government refers to its financial responsibility towards their employees and other developmental planned and unplanned expenditure (Clarida et al, 2002). This component refers to the general price of commodities and services in an economy over a period of time. When the inflation rate rises than it means the purchasing power of per unit of money falls to buy the earlier specified service or product. The important measure of inflation is the consumer price index. The impact of inflation on the economy can be positive as well as negative. The negative effects indicate the opportunity cost of holding back money, the uncertainty of increased inflation in the future might discourage investments and also shortage of commodities and services can occur. The positive effects mean that the centralized banks can adjust the interest rates and encourage the investments in non monetary capital projects on the basis of speculated real time interests (Clarida et al, 2002). Time series is referred to as an array of data points measured at uniform time intervals to analyze meaningful econometric data and predict the future values of the econometric variables. The forecasting for the future is based from the previous values and their movements over a span of time (Shumway, 1988). Arima Models and Regression models are best suited for forecasting and prediction purposes. Often the ordinary least squares regression is used for the estimations of the forecast as the best linear unbiased estimator to arrive at the correct conclusion of the forecast to be made. It helps to predict the value of one variable (which is called the dependant variable) from a set of independent variables that might be correlated either in a positive or negative way to the dependant variable (Vassilis, 2008,Fair, 1996). Aim and Objective of the Study This study will aim to predict the short term interest rates based on the GDP growth rate, inflation rate and the unemployment rate in the United Kingdom. The study will also reflect upon the forecasts and the predictions of the short term interest rates in the future based on the GDP growth rate, inflation rate and the unemployment rates. It will define the monetary policy of a nation and its justification based on regression statistics. Methodology The methodology applied was to first of all collect the data on short term interest rates, the GDP growth rate, inflation rate and the unemployment rate in the United Kingdom from tradeeconomics.com for the period 2008 to 2013 (appendix-1). Then the regression equations were modeled with all these variables coherently at first on the basis of ordinary least squares regression and then the equations were reframed by using elimination of autocorrelation through AR and ARMA models. Each variable was tested to find out whether they were normally distributed or not. Correlation coefficients were evaluated to extrapolate the relationship between the variables and whether the increase in magnitude of one variable increases (positive correlation) or decreases ( negative correlation) the value of the dependant variable under study. The Arma models were used to find out the trend of movement of the variables over a given period of time (2004 to 2013) and specify the future trend or behavior of movement of the dependant variable. The statistical hypothesis testing would be on the results of the p value. A p value more than 0.05 will indicate that out of 100 observations more than 5 observations has happened due to chance factors of random sampling, and the independent variable has no impact or correlation with the dependant variable being studied. On the other hand if the p value or the probability value is less than 0.05 it will indicate that out of 100 observations less than 5 observations has happened due to chance factors of random sampling, and the independent variable created a significant impact on the dependant variable or there is a high and significant correlation of the independent variable with the dependant variable being studied (Dodge, 2003). Results The regression equation of inflation rate, gdp rate and unemployment rate on short term interest rates Model 1: OLS, using observations 2008:01-2014:03 (T = 75) Dependent variable: intrate coefficient std. error t-ratio p-value ---------------------------------------------------------- const 13.1550 0.536937 24.50 2.31e-036 *** une -1.70766 0.0676922 -25.23 3.58e-037 *** gdprate -0.00923772 0.0232157 -0.3979 0.6919 inf 0.284149 0.0661884 4.293 5.49e-05 *** Mean dependent var 1.212000 S.D. dependent var 1.600925 Sum squared resid 18.29796 S.E. of regression 0.507659 R-squared 0.903522 Adjusted R-squared 0.899445 F(3, 71) 221.6394 P-value(F) 5.73e-36 Log-likelihood -53.51919 Akaike criterion 115.0384 Schwarz criterion 124.3083 Hannan-Quinn 118.7398 rho 0.849352 Durbin-Watson 0.334599 Excluding the constant, p-value was highest for variable 4 (gdprate) Anova test for the significance of above regression Analysis of Variance: Sum of squares df Mean square Regression 171.361 3 57.1204 Residual 18.298 71 0.257718 Total 189.659 74 2.56296 R^2 = 171.361 / 189.659 = 0.903522 F(3, 71) = 57.1204 / 0.257718 = 221.639 [p-value 5.73e-036] Prediction of the values as per 95% CI to find the dispersion of data For 95% confidence intervals, t(71, 0.025) = 1.994 intrate prediction std. error 95% interval 2008:01 5.5 4.7 0.54 3.6 - 5.8 2008:02 5.5 4.7 0.54 3.6 - 5.8 2008:03 5.2 4.8 0.54 3.7 - 5.9 2008:04 5.2 4.6 0.53 3.6 - 5.7 2008:05 5.0 5.1 0.54 4.0 - 6.2 2008:06 5.0 4.8 0.53 3.8 - 5.9 2008:07 5.0 4.7 0.53 3.6 - 5.7 2008:08 5.0 4.5 0.53 3.4 - 5.6 2008:09 5.0 4.1 0.53 3.1 - 5.2 2008:10 5.0 4.2 0.55 3.1 - 5.3 2008:11 3.0 3.7 0.53 2.6 - 4.8 2008:12 2.0 3.2 0.53 2.2 - 4.3 2009:01 2.0 2.6 0.53 1.6 - 3.7 2009:02 1.5 2.3 0.52 1.2 - 3.3 2009:03 1.0 1.8 0.52 0.8 - 2.9 2009:04 0.5 1.3 0.53 0.2 - 2.3 2009:05 0.5 0.7 0.53 -0.3 - 1.8 2009:06 0.5 0.4 0.53 -0.7 - 1.4 2009:07 0.5 0.1 0.53 -1.0 - 1.1 2009:08 0.5 0.1 0.53 -1.0 - 1.1 2009:09 0.5 0.0 0.53 -1.1 - 1.1 2009:10 0.5 -0.1 0.53 -1.2 - 0.9 2009:11 0.5 0.1 0.53 -0.9 - 1.2 2009:12 0.5 0.3 0.52 -0.8 - 1.3 2010:01 0.5 0.3 0.51 -0.7 - 1.3 2010:02 0.5 0.3 0.51 -0.7 - 1.3 2010:03 0.5 0.2 0.51 -0.9 - 1.2 2010:04 0.5 0.3 0.51 -0.7 - 1.3 2010:05 0.5 0.4 0.51 -0.6 - 1.4 2010:06 0.5 0.5 0.51 -0.6 - 1.5 2010:07 0.5 0.4 0.51 -0.6 - 1.4 2010:08 0.5 0.5 0.51 -0.5 - 1.6 2010:09 0.5 0.5 0.51 -0.5 - 1.6 2010:10 0.5 0.2 0.52 -0.8 - 1.2 2010:11 0.5 0.2 0.52 -0.8 - 1.2 2010:12 0.5 0.4 0.52 -0.6 - 1.4 2011:01 0.5 0.4 0.52 -0.7 - 1.4 2011:02 0.5 0.6 0.52 -0.4 - 1.6 2011:03 0.5 0.9 0.52 -0.1 - 1.9 2011:04 0.5 1.0 0.52 -0.1 - 2.0 2011:05 0.5 0.9 0.52 -0.1 - 2.0 2011:06 0.5 0.8 0.52 -0.3 - 1.8 2011:07 0.5 0.9 0.52 -0.2 - 1.9 2011:08 0.5 0.9 0.52 -0.1 - 1.9 2011:09 0.5 0.9 0.52 -0.1 - 2.0 2011:10 0.5 0.4 0.53 -0.6 - 1.5 2011:11 0.5 0.4 0.53 -0.7 - 1.4 2011:12 0.5 0.2 0.53 -0.9 - 1.2 2012:01 0.5 -0.2 0.52 -1.2 - 0.9 2012:02 0.5 -0.2 0.52 -1.2 - 0.9 2012:03 0.5 -0.1 0.51 -1.1 - 0.9 2012:04 0.5 0.1 0.51 -0.9 - 1.2 2012:05 0.5 -0.0 0.51 -1.0 - 1.0 2012:06 0.5 0.1 0.51 -0.9 - 1.1 2012:07 0.5 0.2 0.51 -0.8 - 1.2 2012:08 0.5 0.1 0.51 -1.0 - 1.1 2012:09 0.5 0.4 0.51 -0.6 - 1.4 2012:10 0.5 0.5 0.52 -0.6 - 1.5 2012:11 0.5 0.5 0.52 -0.6 - 1.5 2012:12 0.5 0.6 0.51 -0.4 - 1.7 2013:01 0.5 0.6 0.51 -0.4 - 1.6 2013:02 0.5 0.6 0.51 -0.4 - 1.6 2013:03 0.5 0.5 0.51 -0.6 - 1.5 2013:04 0.5 0.6 0.51 -0.4 - 1.6 2013:05 0.5 0.5 0.51 -0.5 - 1.5 2013:06 0.5 0.6 0.51 -0.4 - 1.6 2013:07 0.5 0.6 0.51 -0.4 - 1.7 2013:08 0.5 0.8 0.51 -0.2 - 1.8 2013:09 0.5 0.8 0.51 -0.3 - 1.8 2013:10 0.5 0.9 0.51 -0.1 - 2.0 2013:11 0.5 1.1 0.52 0.1 - 2.2 2013:12 0.5 1.6 0.52 0.6 - 2.6 2014:01 0.5 1.4 0.52 0.4 - 2.4 2014:02 0.5 1.4 0.52 0.3 - 2.4 2014:03 0.5 1.8 0.53 0.8 - 2.9 Forecast evaluation statistics Mean Error 4.2513e-015 Mean Squared Error 0.24397 Root Mean Squared Error 0.49394 Mean Absolute Error 0.39116 Mean Percentage Error -4.5966 Mean Absolute Percentage Error 57.687 Theils U 7.8911 Bias proportion, UM 0 Regression proportion, UR 0 Disturbance proportion, UD 1 Fig A: Representing the 95% CI of short term interest rates versus the forecasts which incorporates seasonality components Fig b: Representing the prediction (forecast) of short term interest rates based on the Model 1 regression seasonality components Test for heteroskedasticity Whites test for heteroskedasticity OLS, using observations 2008:01-2014:03 (T = 75) Dependent variable: uhat^2 coefficient std. error t-ratio p-value ---------------------------------------------------------- const -1.81334 4.41849 -0.4104 0.6829 une 1.47150 1.16479 1.263 0.2110 gdprate 0.0192790 0.379118 0.05085 0.9596 inf -1.42605 0.461662 -3.089 0.0030 *** sq_une -0.134111 0.0828708 -1.618 0.1104 X2_X3 0.0201456 0.0453509 0.4442 0.6584 X2_X4 0.0796301 0.0539932 1.475 0.1451 sq_gdprate 0.00456722 0.00717554 0.6365 0.5267 X3_X4 -0.0613204 0.0280581 -2.185 0.0325 ** sq_inf 0.119996 0.0359030 3.342 0.0014 *** Unadjusted R-squared = 0.481894 Test statistic: TR^2 = 36.142082, with p-value = P(Chi-square(9) > 36.142082) = 0.000037 Summary Statistics of Inf Rate, Interest rates, GDP rates and Unemployment Rates & Test of Normality of their distributions Summary statistics, using the observations 2008:01 - 2014:03 for the variable gdprate (75 valid observations) Mean 0.018667 Median 0.60000 Minimum -6.8000 Maximum 2.8000 Standard deviation 2.7033 C.V. 144.82 Skewness -1.4191 Ex. kurtosis 0.83804 5% percentile -6.4000 95% percentile 2.8000 Interquartile range 1.6000 Missing obs. 0 Test for normality of gdprate: Doornik-Hansen test = 81.4508, with p-value 2.05671e-018 Shapiro-Wilk W = 0.774084, with p-value 2.18827e-009 Lilliefors test = 0.312001, with p-value ~= 0 Jarque-Bera test = 27.3688, with p-value 1.14009e-006 Summary statistics, using the observations 2008:01 - 2014:03 for the variable intrate (75 valid observations) Mean 1.2120 Median 0.50000 Minimum 0.50000 Maximum 5.5000 Standard deviation 1.6009 C.V. 1.3209 Skewness 1.9752 Ex. kurtosis 2.0954 5% percentile 0.50000 95% percentile 5.2000 Interquartile range 0.0000 Missing obs. 0 Test for normality of intrate: Doornik-Hansen test = 292.829, with p-value 2.58861e-064 Shapiro-Wilk W = 0.481303, with p-value 7.71994e-015 Lilliefors test = 0.471747, with p-value ~= 0 Jarque-Bera test = 62.4883, with p-value 2.69678e-014 Summary statistics, using the observations 2008:01 - 2014:03 for the variable inf (75 valid observations) Mean 3.0827 Median 3.0000 Minimum 1.1000 Maximum 5.2000 Standard deviation 0.93799 C.V. 0.30428 Skewness 0.35807 Ex. kurtosis -0.48666 5% percentile 1.6800 95% percentile 4.8400 Interquartile range 1.2000 Missing obs. 0 Test for normality of inf: Doornik-Hansen test = 3.27871, with p-value 0.194105 Shapiro-Wilk W = 0.975284, with p-value 0.149493 Lilliefors test = 0.0768929, with p-value ~= 0.33 Jarque-Bera test = 2.34276, with p-value 0.309939 Summary statistics, using the observations 2008:01 - 2014:03 for the variable une (75 valid observations) Mean 7.5067 Median 7.9000 Minimum 5.2000 Maximum 8.4000 Standard deviation 0.88384 C.V. 0.11774 Skewness -1.5119 Ex. kurtosis 1.0217 5% percentile 5.3000 95% percentile 8.3200 Interquartile range 0.80000 Missing obs. 0 Test for normality of une: Doornik-Hansen test = 100.146, with p-value 1.79267e-022 Shapiro-Wilk W = 0.750813, with p-value 5.88554e-010 Lilliefors test = 0.293241, with p-value ~= 0 Jarque-Bera test = 31.8338, with p-value 1.22286e-007 Finding out ACF and PACF for autocorrelation components LAG ACF PACF Q-stat. [p-value] 1 0.1316 0.1316 0.2308 [0.631] 2 -0.3534 -0.3773 2.1046 [0.349] Forming the AR and ARMAX Models Performing iterative calculation of rho... ITER RHO ESS 1 0.84935 4.35211 2 0.89864 4.08572 3 0.91325 4.05413 4 0.91749 4.05114 5 0.91884 4.05083 6 0.91928 4.05083 Model 2: Cochrane-Orcutt, using observations 2008:02-2014:03 (T = 74) Dependent variable: intrate rho = 0.919284 coefficient std. error t-ratio p-value ------------------------------------------------------- const 3.91376 1.70277 2.298 0.0245 ** une -0.542382 0.216209 -2.509 0.0144 ** gdprate -0.0274469 0.0330541 -0.8304 0.4092 inf 0.228436 0.0738363 3.094 0.0028 *** Statistics based on the rho-differenced data: Mean dependent var 1.154054 S.D. dependent var 1.530618 Sum squared resid 4.050798 S.E. of regression 0.240559 R-squared 0.976342 Adjusted R-squared 0.975328 F(3, 70) 4.686570 P-value(F) 0.004854 rho 0.233602 Durbin-Watson 1.505094 Excluding the constant, p-value was highest for variable 4 (gdprate) Fig C : Represents the AR Model Function evaluations: 97 Evaluations of gradient: 31 Model 3: ARMAX, using observations 2008:01-2014:03 (T = 75) Estimated using Kalman filter (exact ML) Dependent variable: intrate Standard errors based on Hessian coefficient std. error z p-value ------------------------------------------------------- const 4.54782 2.08700 2.179 0.0293 ** phi_1 0.982085 0.0199807 49.15 0.0000 *** theta_1 0.465315 0.115158 4.041 5.33e-05 *** une -0.402972 0.240464 -1.676 0.0938 * gdprate -0.0325518 0.0294175 -1.107 0.2685 inf 0.177283 0.0627334 2.826 0.0047 *** Mean dependent var 1.212000 S.D. dependent var 1.600925 Mean of innovations -0.012586 S.D. of innovations 0.236323 Log-likelihood -0.396000 Akaike criterion 14.79200 Schwarz criterion 31.01442 Hannan-Quinn 21.26943 Real Imaginary Modulus Frequency ----------------------------------------------------------- AR Root 1 1.0182 0.0000 1.0182 0.0000 MA Root 1 -2.1491 0.0000 2.1491 0.5000 ----------------------------------------------------------- FigD: Represents the ARMAX model Regression of Individual components independently on short term interest rates Model 7: OLS, using observations 2008:01-2014:03 (T = 75) Dependent variable: intrate coefficient std. error t-ratio p-value -------------------------------------------------------- une 0.136387 0.0263516 5.176 1.88e-06 *** Mean dependent var 1.212000 S.D. dependent var 1.600925 Sum squared resid 220.1405 S.E. of regression 1.724781 R-squared 0.265782 Adjusted R-squared 0.265782 F(1, 74) 26.78756 P-value(F) 1.88e-06 Log-likelihood -146.7996 Akaike criterion 295.5991 Schwarz criterion 297.9166 Hannan-Quinn 296.5245 rho 0.934573 Durbin-Watson 0.027956 Model 8: OLS, using observations 2008:01-2014:03 (T = 75) Dependent variable: intrate coefficient std. error t-ratio p-value ------------------------------------------------------- gdprate 0.106449 0.0856665 1.243 0.2179 Mean dependent var 1.212000 S.D. dependent var 1.600925 Sum squared resid 293.7017 S.E. of regression 1.992220 R-squared 0.020439 Adjusted R-squared 0.020439 F(1, 74) 1.544063 P-value(F) 0.217937 Log-likelihood -157.6108 Akaike criterion 317.2215 Schwarz criterion 319.5390 Hannan-Quinn 318.1469 rho 0.943293 Durbin-Watson 0.021475 Model 9: OLS, using observations 2008:01-2014:03 (T = 75) Dependent variable: intrate coefficient std. error t-ratio p-value -------------------------------------------------------- inf 0.380229 0.0570562 6.664 4.13e-09 *** Mean dependent var 1.212000 S.D. dependent var 1.600925 Sum squared resid 187.3772 S.E. of regression 1.591265 R-squared 0.375055 Adjusted R-squared 0.375055 F(1, 74) 44.41048 P-value(F) 4.13e-09 Log-likelihood -140.7567 Akaike criterion 283.5134 Schwarz criterion 285.8309 Hannan-Quinn 284.4388 rho 0.925422 Durbin-Watson 0.033186 Seasonality and Augmented Dickey Fuller Tests Model 10: OLS, using observations 2009:01-2014:03 (T = 63) Dependent variable: intrate coefficient std. error t-ratio p-value ----------------------------------------------------------- inf 0.149258 0.0143852 10.38 9.56e-015 *** gdprate -0.00943846 0.0426130 -0.2215 0.8255 sd_une -0.251617 0.0881084 -2.856 0.0060 *** sd_intrate -0.219515 0.0513248 -4.277 7.31e-05 *** sd_inf -0.00380669 0.0223834 -0.1701 0.8656 sd_gdprate 0.00735892 0.0111610 0.6593 0.5123 Mean dependent var 0.547619 S.D. dependent var 0.232696 Sum squared resid 2.582789 S.E. of regression 0.212866 R-squared 0.883920 Adjusted R-squared 0.873737 F(6, 57) 72.33981 P-value(F) 7.86e-25 Log-likelihood 11.22621 Akaike criterion -10.45242 Schwarz criterion 2.406385 Hannan-Quinn -5.394991 rho 0.539113 Durbin-Watson 0.421813 P-value was highest for variable 7 (sd_inf) Augmented Dickey-Fuller test for intrate including one lag of (1-L)intrate (max was 11, criterion modified AIC) sample size 73 unit-root null hypothesis: a = 1 with constant and quadratic trend plus seasonal dummies model: (1-L)y = b0 + b1*t + b2*t^2 + (a-1)*y(-1) + ... + e 1st-order autocorrelation coeff. for e: 0.023 estimated value of (a - 1): -0.0708644 test statistic: tau_ctt(1) = -1.80373 asymptotic p-value 0.8824 Fig E: After consideration of seasonality the smoothed and original short term interest rates are plotted. Discussion & Conclusion The policy is dependant on the rates of interest in an economy, which means this determines the price at which the money might be borrowed and determines the total supply of money. Monetary policy influences various components like economic growth (GDP growth rate), inflation , the exchange rates with other currencies and the unemployment status of a country. The monetary policy is jeopardized if the rates of interest are high and the supply of money in the market decreases. While the policy is referred to as expansionary when the interest rates are reduced and the money supply to the market increases. Monetary policy is the process by which the government of the country, the monetary authority or centralized banks of a country controls the flow and availability of money and at the same time the cost of money or the rate of interest designed to achieve a set of objectives oriented to increase the growth and foster the stability of economy of a country. Thus the interest rates and the monetary policy are important attributes for the policy makers to take credible decisions. If the private companies believe that the policy makers are aiming to reduce the inflation then they will anticipate lowering of prices for their commodities or services in the future and rationalize their profitable expectations The variables used in this study were not normally distributed except for inflation rate which had normal distribution with a p value of more than 0.05 which meant the values were from the same population and had an equal distribution of scores in all the ranges and the distribution was not skewed before the regression statistics but the data of short term interest rates, unemployment rate and GDP were skewed. In the OLS model reflected the prediction statistics whenever the unemployment rate is going to increase the short term interest rates will significantly fall and though the short term interest rates will further be lowered if GDP decreases and decreasing short term interest rates will decrease inflation on check and low further creating borrowing of money from the banks and hence investment in manpower and capital machinery thus decreasing the unemployment rate. It was observed that short term interest rates in UK will decrease whenever the unemployment rates will rise and will increase with inflation and it will decrease with increased GDP but the correlation was not statistically significant. This prediction of the above was confirmed both by the OLS formed together with all variables and individually regressing each GDP growth rate , inflation rate and unemployment rate on short term interest rates. The autoregressive moving average model or ARMA provides a description in terms of two polynomials, one is the auto-regression component (AR) and the other moving average (MA) component and was described by Box Jenkins. In a given time series the ARMA model helps to understand the prediction of future values. In the AR component when the phi parameters are less than one the processes are stationary and when it is more than 1 the model is not stationary. The moving average model is a finite impulse response filter and the error terms or white noise will be assumed to be the independent identically distributed random variables which are sampled from a normal distribution and will have a variance =0. The ARMA model was fitted to the regression model in our study by finding the appropriate assumptions of the partial autocorrelation functions (p) for the AR part and the autocorrelation (functions (q) for the MA. The ARMA model describes the system as a function of the unobserved shocks which means the short term interest rates may be shocked by fundamental information and exhibits reversion effects due to the market variants. Even after making assumptions for the phi and theta components the regression equation was similar to the basic regression equation where it was once again reflected that whenever unemployment rates will increase the short term interest rates has a trend to decrease and whenever shot term interest rates will increase inflation will increase (Vassilis, 2008,Fair, 1996). Hence the reproducibility of the uniform model through the ordinary least squares regression, AR model, ARMAX model justifies the validity of the model and is a good one in predicting future values of short term interest rates based on inflation rates and unemployment rates. The autocorrelation functions (ACF) and the partial autocorrelation functions (PACF) on the differenced series indicated the justifiable AR or MA terms that are needed. The PCF means that amount of correlation that cannot be explained by their mutual correlation with other defined sets of variables. PACF specifies the lag component in itself which are not explained by the lower orders of lag. As the PACF of the differenced series displayed a sharp cut off and the autocorrelation was positive AR term was included in the regression model(Vassilis, 2008,Fair, 1996). This eliminated the autocorrelation component of the OLS initially constructed and justified the initial OLS model where once again it was found in the AR model that whenever the unemployment rate is going to increase the short term interest rates will significantly fall and though the short term interest rates will further be lowered if GDP decreases and decreasing short term interest rates will keep inflation on check and low further creating borrowing of money from the banks and hence investment in manpower and capital machinery thus decreasing the unemployment rate. The federal governments lay down the monetary policies by adjusting short term interest rates. This will affect the money lending rate and other interest rates which will affect unemployment, inflation and consumer confidence. Unemployment rate is one of the key factor in influencing the monetary policy of a nation. As in our analysis there was a significant negative correlation between unemployment rate and short term interest rates, it indicated that whenever the unemployment rate rises there is a trend to lower the short term interest rates. This is because low interest rates will stimulate the economy. Labor demand and supply of manpower will increase whenever the short term interests will fall as money would be borrowed from the banks to set up new projects thus opening up jobs. When the economy picks up the Government alters the interest rates to keep the inflation in check. As can be seen from the fig it is evident as the unemployment levels have remained high and increased from 2009 the short term interest rates have fallen to combat unemployment rates and have remained constant till 2013 correlating with the steady constancy of unemployment rates (Corsetti, 2011). The ARMA or the autocorrelation and moving average model helps to predict the future trend of a variable (in this case the short term interest rates) after considering the allowances for autocorrelation with other variables and seasonality in a time series analysis and makes a forecast strong enough to formulate the policies in future that will affect the economy of a nation and at the same time protecting the vested interest of its citizens in a positive way. References Cf. Clarida, R., Galí, J., Gertler, M. (2002). A simple framework for international policy analysis. Journal of Monetary Economics, 49(4), pp. 879-904. Corsetti, G., Pesenti, P. (2005). International dimensions of optimal monetary policy. Journal of Monetary Economics, 52(2), pp. 281-305 Corsetti, G., Dedola, L., Leduc, S. (2011). Optimal Monetary Policy in Open Economies. In B.M. Friedman and M. Woodford (Eds.). Handbook of Monetary Economics, vol. III. Amsterdam: Elsevier. Devereux, M.B., Engel, C. (2003). Monetary policy in the open economy revisited: Price setting and exchange rate flexibility. Review of Economic Studies, 70(4), pp. 765-783. Dodge, Y. (2003). The Oxford Dictionary of Statistical Terms. New York: Oxford University Press Fair,R (1996). "Computational Methods for Macroeconometric Models," Handbook of Computational Economics, v. 1, pp[1]-169. Shumway, R. H. (1988). Applied statistical time series analysis. Englewood Cliffs, NJ: Prentice Hall. Vassilis A. Hajivassiliou (2008). "computational methods in econometrics," The New Palgrave Dictionary of Economics, 2nd Appendix-1 une 2008:01 5.3 2008:02 5.3 2008:03 5.3 2008:04 5.4 2008:05 5.2 2008:06 5.4 2008:07 5.6 2008:08 5.8 2008:09 6.0 2008:10 6.1 2008:11 6.3 2008:12 6.5 2009:01 6.7 2009:02 6.9 2009:03 7.2 2009:04 7.4 2009:05 7.7 2009:06 7.9 2009:07 8.0 2009:08 8.0 2009:09 8.0 2009:10 8.0 2009:11 7.9 2009:12 7.9 2010:01 8.1 2010:02 8.1 2010:03 8.1 2010:04 8.1 2010:05 8.0 2010:06 8.0 2010:07 8.0 2010:08 7.9 2010:09 7.9 2010:10 8.1 2010:11 8.1 2010:12 8.0 2011:01 8.1 2011:02 8.0 2011:03 7.9 2011:04 7.8 2011:05 7.9 2011:06 8.0 2011:07 7.9 2011:08 7.9 2011:09 7.9 2011:10 8.3 2011:11 8.3 2011:12 8.4 2012:01 8.4 2012:02 8.4 2012:03 8.3 2012:04 8.2 2012:05 8.2 2012:06 8.1 2012:07 8.0 2012:08 8.1 2012:09 7.9 2012:10 7.8 2012:11 7.8 2012:12 7.7 2013:01 7.8 2013:02 7.8 2013:03 7.9 2013:04 7.8 2013:05 7.8 2013:06 7.8 2013:07 7.8 2013:08 7.7 2013:09 7.7 2013:10 7.6 2013:11 7.4 2013:12 7.1 2014:01 7.2 2014:02 7.2 2014:03 6.9 inf 2008:01 2.2 2008:02 2.2 2008:03 2.5 2008:04 2.5 2008:05 3.0 2008:06 3.3 2008:07 3.8 2008:08 4.4 2008:09 4.3 2008:10 5.2 2008:11 4.5 2008:12 4.1 2009:01 3.1 2009:02 3.0 2009:03 3.2 2009:04 2.4 2009:05 2.3 2009:06 2.2 2009:07 1.8 2009:08 1.8 2009:09 1.6 2009:10 1.1 2009:11 1.5 2009:12 1.9 2010:01 3.5 2010:02 3.5 2010:03 3.0 2010:04 3.4 2010:05 3.3 2010:06 3.4 2010:07 3.2 2010:08 3.1 2010:09 3.1 2010:10 3.1 2010:11 3.2 2010:12 3.3 2011:01 3.7 2011:02 4.0 2011:03 4.4 2011:04 4.0 2011:05 4.5 2011:06 4.5 2011:07 4.2 2011:08 4.4 2011:09 4.5 2011:10 5.2 2011:11 5.0 2011:12 4.8 2012:01 3.6 2012:02 3.6 2012:03 3.2 2012:04 3.5 2012:05 3.0 2012:06 2.8 2012:07 2.5 2012:08 2.6 2012:09 2.5 2012:10 2.2 2012:11 2.2 2012:12 2.2 2013:01 2.7 2013:02 2.7 2013:03 2.8 2013:04 2.8 2013:05 2.4 2013:06 2.7 2013:07 2.9 2013:08 2.8 2013:09 2.7 2013:10 2.7 2013:11 2.2 2013:12 2.1 2014:01 2.0 2014:02 1.9 2014:03 1.7 intrate 2008:01 5.5 2008:02 5.5 2008:03 5.2 2008:04 5.2 2008:05 5.0 2008:06 5.0 2008:07 5.0 2008:08 5.0 2008:09 5.0 2008:10 5.0 2008:11 3.0 2008:12 2.0 2009:01 2.0 2009:02 1.5 2009:03 1.0 2009:04 0.5 2009:05 0.5 2009:06 0.5 2009:07 0.5 2009:08 0.5 2009:09 0.5 2009:10 0.5 2009:11 0.5 2009:12 0.5 2010:01 0.5 2010:02 0.5 2010:03 0.5 2010:04 0.5 2010:05 0.5 2010:06 0.5 2010:07 0.5 2010:08 0.5 2010:09 0.5 2010:10 0.5 2010:11 0.5 2010:12 0.5 2011:01 0.5 2011:02 0.5 2011:03 0.5 2011:04 0.5 2011:05 0.5 2011:06 0.5 2011:07 0.5 2011:08 0.5 2011:09 0.5 2011:10 0.5 2011:11 0.5 2011:12 0.5 2012:01 0.5 2012:02 0.5 2012:03 0.5 2012:04 0.5 2012:05 0.5 2012:06 0.5 2012:07 0.5 2012:08 0.5 2012:09 0.5 2012:10 0.5 2012:11 0.5 2012:12 0.5 2013:01 0.5 2013:02 0.5 2013:03 0.5 2013:04 0.5 2013:05 0.5 2013:06 0.5 2013:07 0.5 2013:08 0.5 2013:09 0.5 2013:10 0.5 2013:11 0.5 2013:12 0.5 2014:01 0.5 2014:02 0.5 2014:03 0.5 gdprate 2008:01 2.8 2008:02 2.8 2008:03 2.8 2008:04 2.8 2008:05 2.8 2008:06 2.8 2008:07 0.6 2008:08 0.6 2008:09 0.6 2008:10 -2.1 2008:11 -2.1 2008:12 -2.1 2009:01 -4.3 2009:02 -4.3 2009:03 -4.3 2009:04 -6.8 2009:05 -6.8 2009:06 -6.8 2009:07 -6.3 2009:08 -6.3 2009:09 -6.3 2009:10 -5.0 2009:11 -5.0 2009:12 -5.0 2010:01 0.5 2010:02 0.5 2010:03 0.5 2010:04 0.5 2010:05 0.5 2010:06 0.5 2010:07 2.0 2010:08 2.0 2010:09 2.0 2010:10 2.4 2010:11 2.4 2010:12 2.3 2011:01 1.8 2011:02 1.8 2011:03 1.8 2011:04 1.7 2011:05 1.7 2011:06 1.7 2011:07 0.8 2011:08 0.8 2011:09 0.8 2011:10 1.0 2011:11 1.0 2011:12 1.0 2012:01 0.6 2012:02 0.6 2012:03 0.6 2012:04 0.6 2012:05 0.6 2012:06 0.6 2012:07 0.1 2012:08 0.1 2012:09 0.1 2012:10 0.3 2012:11 0.3 2012:12 0.3 2013:01 0.2 2013:02 0.2 2013:03 0.2 2013:04 0.5 2013:05 0.5 2013:06 0.5 2013:07 1.7 2013:08 1.7 2013:09 1.7 2013:10 1.8 2013:11 1.8 2013:12 1.8 2014:01 2.3 2014:02 2.3 2014:03 2.3 Read More