The economist and policymakers are often keen to know the trends and correlations of the inflation rate, interest rate, literacy rate and unemployment rate that may help them to analyze the economic growth of a country. Inflation refers to a situation where the supply of money exceeds its demand or prices of commodities increase steadily. Often, inflation puts adverse consequences on the purchasing power of the people,

where

In literature, a variety of techniques have been proposed for the forecasting of these economic factors that range from the simple linear models to more sophisticated nonlinear or time series models. Such models have often been used to either study the time-dependent behavior of each of the individual factors or the mutual dependence of one or many variables on another set of variables.

Pakistan is the 6^{th} largest population in the world having about 65 million labors that makes it the 10^{th} largest labor force. Due to the rapid increase in population and fewer job opportunities the government needs to properly forecast economic factors like inflation, interest, literacy and unemployment to construct future policies. In order to analyze the impact of such factors on the socio-economic growth of Pakistan many studies including

In order to construct the statistically and logically feasible nonlinear models for the time-dependent inflation rate, interest rate (in Pakistan, it is specifically termed as Karachi interbank offered rate, commonly known as Kibor rate) literacy rate and the unemployment rate the relevant secondary data from 2001 to 2019 was collected from the different sources like Pakistan Bureau of Statistics, International Labor Organization and World Bank

The method of nonlinear least squares is applied to fit the data

where ^{2}) and the adjusted R^{2} are given in

Estimated Coefficients of the model |
95% confidence bounds |

a1 = 12.67 |
(-1.771e+05, 1.771e+05) |

SSE RMSE R-square Adjusted R-square 0.7312 0.8551 0.9975 0.9548

Estimated Coefficients of the model 95% confidence bounds a0 = 9.916 (9.019, 10.81) (0.3231, 1.98)

SSE RMSE R-square Adjusted R-square 10.71 0.9078 0.902 0.8643

Estimated Coefficients of the model 95% confidence bounds a1 = 192 (-1.429e+04, 1.467e+04)

SSE RMSE R-square Adjusted R-square 2.127 0.7404 0.9842 0.9781

Estimated Coefficients of the model 95% confidence bounds a = 3.876 (-364.5, 372.2)

SSE RMSE R-square Adjusted R-square 1.92 0.5295 0.9159 0.7837

The inflation rate, interest rate (Kibor), literacy rate and unemployment rates of Pakistan from the fiscal year 2001 to 2019 have been modeled and compared with the observed values of each variable. Using the modeled equations the forecasting rates for the next ten years from 2020 to 2029 has been smoothly determined. ^{st} fiscal year to the 19^{th} fiscal year of 21^{st} century. The fitted values are very close to the observed values also show the smoothness with respect to time. The next ten years forecasting results exhibit a smooth trend that fluctuates approximately between inflation rates 6 to 15. Thus, on the basis of the last 19 years data and the fitted model (Eq.5) the inflation rate in Pakistan is expected to reach a height of about 15% in 2023 than expected to decrease smoothly by 2029 with some rise and fall.

Method of non-linear least squares was employed to fit the best regression models for the inflation rate, interest rate (Kibor), literacy rate and unemployment rate of Pakistan. Various types of nonlinear algebraic and transcendental functions were worked out. After extensive regression analysis, it was found that the sum of sines model with five general terms, the Fourier model with two general terms, the sum of sines model with two general terms and a mix of the Gaussian model and other custom expressions are the finest types of models for the inflation rate, interest rate, literacy rate and the unemployment rate of Pakistan respectively. The next ten years forecasting trends have shown that the inflation rate, interest rate, and unemployment rate are expected to be higher in the years 2023 and 2024, while the literacy rate is expected to be optimistic in the next ten fiscal years. As the high inflation rate, interest rate and unemployment rate put a negative impact on the economy of any nation, therefore, the government should take necessary actions to reduce the expected and unwanted variations in these socio-economic factors. The future work will focus on the modeling of the interrelationships among inflation rate, interest rate (Kibor), literacy rate and the unemployment rate of the Pakistan for first few decades of 21^{st} century.

We acknowledge the University of Sindh, Jamshoro and the Quaid-e-Awam University of Engineering, Science and Technology, Nawabshah for providing the facilities and resources to conduct this research.