یہ عشق میں نہ سوچ، تُجھے کیا نہیں ملا
ہے کر لیا، تو خاک میں اپنی جبیں ملا
ہم راہ دیکھتے ہی رہے جس کی عمر بھر
آیا وہ شہر میں بھی تو ہم سے نہیں ملا
بچپن میں دل کی بستی میں رہتے تھے کتنے لوگ
دیکھا شباب میں تو فقط اک مکیں ملا
اگلے جہاں کے عہد پہ ہم کو دیا ہے ٹال
کم بخت ہم کو وہ تو بلا کا ذہیں ملا
کہتے رہے تھے یار جسے ہم تمام عمر
اک دن عدو کی بزم میں وہ نازنیں ملا
گر یاں دیا نہ تُو نے تو نہ لوں گا حشر میں
یارب اسے اگر ہے ملانا، یہیں ملا
This article addresses the Gross Domestic Product (GDP) growth rate, normally used to determine how quickly economic growth has contracted in a region, i.e. Adverse growth. Thus, the Finance Ministers and the ASEAN Central Bank Governors have decided on a number of promises, including (1) that exceptional policy responses to resolve this pandemic would be washed away to restore economic activity. (2) to enhance the economic and financial monitoring efficiency of the area, and to promote readiness to act as an efficient financial safety net in the region and as an essential component of the global financial security net of the Chiang May Initiative Multilateralization (CMIM). (3) to facilitate greater intra-ASEAN exchange and investment by setting up eligible ASEAN banks (4) funding for local currency use programs for settlements, foreign investments and other operations between ASEAN countries, such as revenue and transfer transactions. (5) supports the advancement of partnership in the area of the funding of infrastructures, in the context of many recommendations to facilitate private investment growth, among other steps. (6) to promote initiatives to use digital financial services to enhance the financial inclusion of the area and to enhance cooperation on various cyber risk management material.
The bootstrap methods are used extensively in statistical analysis of econometric and time series models. In small sample situations, where the asymptotic theory does not work well to approximate the unknown sampling distribution of a statistic, bootstrap methods are used as an alternative. The idea is that the observed sample contains useful information about the population characteristics and resampling from it can give a good approximation to the sampling distribution. Therefore, bootstrap approximations can provide better small sample performance than those obtained from asymptotic theory. The main focus of the present work is the application of bootstrap methods to time series models. The current study has three dimensions. The first part is concerned with the construction of bootstrap prediction intervals for autoregressive fractionally integrated moving-average processes which is a special class of long memory time series. For linear short-range dependent time series, the bootstrap based prediction interval is a good nonparametric alternative to those constructed under parameter assumptions. In the long memory case, we use AR-sieve bootstrap which approximates the data generating process of a given long memory time series by a finite order autoregressive process and resample the residuals. For the construction of prediction intervals, we applied two sieve bootstrap algorithms. A simulation study is conducted to examine and compare the performance of these AR-sieve bootstrap procedures. We use four different values of the long memory parameter d.For the purpose of illustration a real data example is also presented. In second part of this work, we propose two bootstrap procedures to construct prediction intervals for ARFIMA-GARCH models. The first method is based on the model based bootstrap, in which the order of the model is assumed to be known. The second bootstrap method is based on the idea of approximating the ARFIMA part by an AR model. In modeling the ARFIMA-GARCH model, the first step is to determine the order of ARFIMA part. Determination of the order of ARFIMA model is a complicated task. To simplify the model building procedure, we approximate the ARFIMA part of the ARFIMA-GARCH model by an AR(p) model and fit an AR-GARCH model instead of ARFIMA-GARCH model. The third part of this thesis is based on testing goodness-of-fit in Autoregressive fractionally integrated moving-average models with conditional hetroscedasticity. We extend the applicability of Hong’s and power transformed Hong’s test statistics as goodness-of-fit tests in ARFIMA-GARCH models where the structural form of GARCH model is unknown. Simulation study is performed to assess the size and power performance of both tests.