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Lifetime distributions are mostly Weibull, exponential, gamma and lognormal, and these observations may be correlated. For lifetime improvement experiments, optimal settings of the operating conditions are identified using D-optimal, or rotatable designs. Therefore, for correlated lifetime observations with different distributions, locating the optimal operating settings is the primary requirement to the quality engineers. The current report derives some efficient rotatable designs for autocorrelated and a particular form of compound symmetry correlated error structures for the above mentioned four lifetime distributions. Note that the derived designs depend on the concerned correlated error structure but free of correlation coefficient values and the lifetime distributions..

Keywords: Autocorrelated errors; Compound symmetry structure; Invariably designs; Lifetime distributions; Mean lifetime model; Robust first-order rotatability.

Electricity markets are affected by rapidly changing structures, in particular due to the increasing share of renewable energies. Hence, the use of stationary time series models for modelling spot prices becomes moreand more questionable. As a step towards the tractability of non-stationary time series we introduce in this paper a new class of stochastic processes which can be used in situations where the time series data at hand exhibit a non-stationary behaviour. These processes behave locally like classical ????-stable processes although the parameters can vary over time. We illustrate the estimation of such processes using a straightforward maximum likelihood approach. Moreover, we show how the model can be applied to electricity spot prices. The approach of the paper can be transferred to other areas of applications and, therefore, should open the door to a new way of handling real-life phenomena with nonstationary behavior.

Keywords: Electricity prices-independent increment process-non-stationary process-time-varying parameters.

Forecasting inflation is the key but challenging task for the monetary authority that aims to stabilise price level conducive for sustained economic growth. The standard autoregressive models overly depend on inter-temporal macro variables and their lags rendering inaccurate estimation and poor forecast accuracy. The Bayesian vector autoregression (BVAR) estimation allows more endogenous variables and prior information and enables more accurate inflation forecasts. This paper forecasts inflation over short horizons (up to 6 quarters ahead) using the quarterly data from Q2- 1996 to Q1-2019 data applying the BVAR method with rolling and expanding window forecast strategies. The best prior is selected by comparing the outof-sample forecast accuracy. Two BVAR models that describe the important dynamics and interactions between the determinants of inflation are estimated. The BVAR model is compared with other benchmark models. The BVAR inflation forecasting outperforms the benchmark univariate and VAR models. The fan charts for modelling inflation through the Bayesian VAR model show that the model delivers a decent performance and can be used to forecast inflation for short-horizons.

Keywords: Inflation, forecasting, Bayesian vector autoregression, forecast evaluation

JEL classification: B23, C11, C53, E31, E37

In the world economic history, gold has been acting as a fundamental character as a universally expensive useful commodity. Gold has possessed a unique social rank of the human race for millennia which has a long history as a costly metal and its history is far from over. Its natural beauty, luster, brilliance, resistance to tarnish and high malleability make it enjoyable to work and play. So, the production of gold has been started long years ago by the human race. The history of gold production data was not consistent, as they were reported in many books or diaries. Note that any historical data set is not accurate as a scientific experiment, or measurement data. It is highly important to study history with unbiased historical data which can only be obtained by using some scientific modeling method from the raw available data. The current article aims to study the history of Spanish and Portuguese colonies’ gold production trends from 1492 to 1810 statistically. The report not only develops the efficient estimates of gold production during this period, but also examines the depression status in the gold mining industry, and many historical events such as the early industrial advancement, industrial revolution that were related with this industry. All the events are located from the developed parametric and non-parametric models, while the non-parametric model gives better estimates.

Keywords: Ancient history of gold; Cubic spline; Gold production trend; Joint generalized linear models; Spanish and Portuguese colonies.

This paper introduces the trading volume of the share price into the neural network in an attempt to test if an exogenous variable, in the form of trading volume, can produce more accurate results compared to only having the closing price fed into the neural network. By feeding the volume into the neural network we can understand if human behaviour and action can affect the future of that share price and the significance of its effect on the future price. By feeding the volume into the network, we can also compare how a greater number of trading days, weeks, months, quarters and years affect the future share price. This may clarify whether higher or lower volumes of trading result in better forecasting accuracy. Comparisons can also be drawn for when the trading volume is being fed into the network and when it is not.

Keywords: Neural Networks; Forecasting; Prediction; Trading;

In this paper, we discuss the Generalized Type II censoring scheme for the Log-Logistic distribution and obtain the Maximum Likelihood Estimate of unknown parameters. The Maximum Likelihood equations are not mathematically tractable, we use the Newton Raphson iterative procedure to obtain estimate of scale parameters, their variance covariance matrix, reliability function and hazard rate for both known and unknown shape parameters. Further, Likelihood Ratio test is used for testing the homogeneity of several scale parameters of the log logistic distribution. Monte-Carlo simulation is performed to study performance of estimates of parameters. We also carried out cost of experiment for the generalized type II censoring.

Keywords: Generalized Type II censoring, Log-Logistic distribution, Maximum Likelihood Estimation, Likelihood Ratio Test, Cost Function