Ex-post andex-ante prediction of unobserved economic time series: a case study

Abstract

In several countries, some macro-economic variables are not observed frequently (e.g. quarterly) and economic authorities need estimates of these high-frequency ®gures to make econometric analyses or to follow closely the country's economic growth. Two problems are involved in this context. The ®rst is to make these estimates after observing low-frequency values and some related indicators, and the second is to obtain predictions using just the observed indicators, i.e. before observing a new low-frequency ®gure. This paper gives a new optimal solution to the ®rst problem, and solves the second using a recursive optimal approach. In the second situation, additionally, statistical tests are developed for detecting structural changes at current periods in the macro-economic variable involved.

A Coincident Index for the State of the Economy*

“…The reader can see the details in Nieto's (1998) paper. The test is carried out using as data the residuals Ç b t obtained from fitting model (2b) and the series É e t and as test statistic the classical Ljung-Box Q statistic or the F-Statistic in a pairwise Granger-causality test.…”

“…Two cases are analyzed: (i) there are no observations for W t in the time interval mn ½ mºn ½» , and (ii) for some i ½ m, we have observed W mn ½ W mn i . It is worth noticing that one should not consider the prediction of Z t for t mºn ½» because once Y n ½ is observed, one must adjust the last predictions between observation times mn ½ and mºn ½» using the ex post recursive procedure described by Nieto (1998) and then to repeat the ex ante exercise for t mºn ½» ½ mºn ¾»; and so on. At this point it is important to remark that with the ex post recursive procedure just mentioned, the predicted figures of the target process up to time mn do not need to be changed as a new annual figure becomes available.…”

“…Notice that if t and t are deterministic, then º½½» reduces to Equation (10) of Nieto (1998). Also notice that computation of MSEº Ç Z t n » is very important because with this value one can obtain a ½¼¼º½ « » ± prediction interval for Z t , where ¼ « ½.…”

“…This exercise was also done by Nieto (1998) The set of economic indicators for obtaining the observed series Û t was: cement production (CP, thousands of tons), oil production (OP, thousands of barrels), total consumption of electric power and gas (EPG, MW/hour), and the manufacturing production index without including coffee (MPI). Assembling of the data set was performed by Banco de la Republica (BR), the Colombian Central Bank.…”

“…In this paper, Nieto's (1998) approach is extended in order to design a coincident index for the state of an economy. The extension consists in replacing the deterministic component by stochastic structural components (Harvey, 1989).…”