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This survey focuses on two families of nonlinear vector time series models, the family of vector threshold regression (VTR) models and that of vector smooth transition regression (VSTR) models. These two model classes contain incomplete models in the sense that strongly exogeneous variables are allowed in the equations. The emphasis is on stationary models, but the considerations also include nonstationary VTR and VSTR models with cointegrated variables. Model specification, estimation and evaluation is considered, and the use of the models illustrated by macroeconomic examples from the literature.

This paper aims to empirically test for multiple cointegrating vectors in a holistic manner. Theoretical developments imply bivariate cointegration among stock prices, dividends, output and consumption where independent models identify key theoretical cointegration vectors.

This paper considers both Johansen and Horvath–Watson testing approaches for cointegration. This paper also examines the forecasting power of these cointegrating relationships against alternate forecast variables.

The results suggest evidence of a long-run cointegrating relationship between stock prices, dividends, output and consumption, although not necessarily linked by a single common stochastic trend; each series responds to disequilibrium with greater evidence of a reaction from dividends and consumption – of note, output responds to changes in stock market equilibrium; and there is forecast power from the joint stock market–macro cointegrating vector for stocks returns and consumption growth over the historical average. Of particular note, other forecast models that include consumption perform well and suggest a key role for this variable in stock return and consumption growth forecasts.

This is the first paper to combine the cointegrating relationships between stocks, dividends, output and consumption. Thus, the empirical validity of stated theoretical hypotheses can be analysed. The forecast results also demonstrate the usefulness of this. They also show that forecast models that include consumption perform well and suggest a key role for this variable in stock return and consumption growth forecasts.

The “Fed Model” postulates a cointegrating relationship between the equity yield on the S&P 500 and the bond yield. We evaluate the Fed Model as a vector error correction forecasting model for stock prices and for bond yields. We compare out-of-sample forecasts of each of these two variables from a univariate model and various versions of the Fed Model including both linear and nonlinear vector error correction models. We find that for stock prices the Fed Model improves on the univariate model for longer-horizon forecasts, and the nonlinear vector error correction model performs even better than its linear version.

This study examines the dynamic responses of five different daily energy prices to a pulse shock affecting the daily price of oil.

Daily data for energy prices from the Federal Reserve Economic Data (FRED) database for January 7, 1997, through February 8, 2021, are analyzed. A bivariate structural vector error correction model and generalized autoregressive conditionally heteroscedastic model are combined and extended by adding the volatility of the growth rate of daily oil prices as an explanatory variable for the growth rates of energy prices. This model is estimated and used to generate impulse responses for energy prices.

The empirical results show that the levels of the daily energy prices examined have unit roots, are integrated of order one, are cointegrated, and generally revert slowly to their long-term equilibrium relationships with the price of oil. The growth rates for the daily energy prices have autoregressive conditional heteroscedasticity, generally are positively related to the volatility of daily oil prices, respond quickly to a pulse shock to daily oil prices, and have cumulative responses that last at least one month.

This paper allows for simultaneous estimation of extended bivariate structural vector error correction and generalized autoregressive conditionally heteroscedastic models that include the volatility of oil as an explanatory variable and uses these models to generated cumulative impulse responses for the growth rates of daily energy prices to oil price shocks.

It is widely documented that while contemporaneous spot and forward financial prices trace each other extremely closely, their difference is often highly persistent and the conventional cointegration tests may suggest lack of cointegration. This chapter studies the possibility of having cointegrated errors that are characterized simultaneously by high persistence (near-unit root behavior) and very small (near zero) variance. The proposed dual parameterization induces the cointegration error process to be stochastically bounded which prevents the variables in the cointegrating system from drifting apart over a reasonably long horizon. More specifically, this chapter develops the appropriate asymptotic theory (rate of convergence and asymptotic distribution) for the estimators in unconditional and conditional vector error correction models (VECM) when the error correction term is parameterized as a dampened near-unit root process (local-to-unity process with local-to-zero variance). The important differences in the limiting behavior of the estimators and their implications for empirical analysis are discussed. Simulation results and an empirical analysis of the forward premium regressions are also provided.

This paper aims to empirically examine how shocks to monetary policy measures (the short-term nominal interest rate and broad money supply) affect macroeconomic aggregates, namely, output growth of the economy, national price levels and the nominal exchange rate.

Johansen’s (1995) cointegration technique and error correction models are used to explore the long-run relationship among variables. To investigate how macroeconomic aggregates respond to a one-standard deviation shock to the underlying monetary measures, the authors estimate impulse response functions based on error correction models. The study uses quarterly data covering the period 1980-2009.

The results provide evidence that there is a long-run stable relationship between the authors' monetary measures and the underlying macroeconomic aggregates. They also find that the industrial production adjusts at a faster speed relative to commodity prices and the exchange rate over the examined period. Further, they show that the short-term interest rate has relatively stronger effects on output as compared to broad money supply, whereas prices and exchange rates adjust more quickly to their long-run equilibrium when money supply is used as a measure of monetary policy. Finally, the authors find significant evidence of a price puzzle regardless of whether they consider a closed or an open economy case. However, an initial appreciation of exchange rate is observed in response to a one-standard deviation shock to money supply, indicating the overshooting hypothesis phenomenon.

The findings of the analysis suggest that the interest rate-oriented monetary policy is more effective when the monetary authorities’ objective is to enhance the output growth of the economy. However, in case of inflation targeting, the broad money supply seems a more appropriate instrument. Our findings also suggest that the monetary policy has a significant role in stabilizing both real and nominal sectors of the economy.

The main value of this paper is to examine the significance of monetary policy for a developing and relatively small open economy, namely, Pakistan. The authors use the error correction model, which improves the estimation by accounting for the long-run association. They also take into account the world oil prices by including the world commodity price index as a control variable in their empirical investigation. Finally, they utilize quarterly data rather than annual, and they cover a relatively recent sample period.

Vector error-correction models (VECMs) have become increasingly important in their application to financial markets. Standard full-order VECM models assume non-zero entries in all their coefficient matrices. However, applications of VECM models to financial market data have revealed that zero entries are often a necessary part of efficient modelling. In such cases, the use of full-order VECM models may lead to incorrect inferences. Specifically, if indirect causality or Granger non-causality exists among the variables, the use of over-parameterised full-order VECM models may weaken the power of statistical inference. In this paper, it is argued that the zero–non-zero (ZNZ) patterned VECM is a more straightforward and effective means of testing for both indirect causality and Granger non-causality. For a ZNZ patterned VECM framework for time series of integrated order two, we provide a new algorithm to select cointegrating and loading vectors that can contain zero entries. Two case studies are used to demonstrate the usefulness of the algorithm in tests of purchasing power parity and a three-variable system involving the stock market.

The purpose of this paper is to examine the structure and dynamics of Singapore's Central Area office market. A long-run equilibrium relationship is tested and a short-run adjustment error correction model are estimated, incorporating appropriate serial error correction. The long-run equation is estimated for office rent, with office employment and available stock.

With the vector error correction model (VECM), the lagged rent, available stock, office employment, vacancy and occupied stock (OS) can impact the rental adjustment process. Equilibrium rent on the whole reacts positively to lagged rents, available stock, office employment, OS and negatively to vacancy rates (VC). Past levels of positive change in VC and rental growth can have negative effects on current OS.

While good economic conditions signaled by increases in rents increase the supply of new stock (available space), higher rents and VC dampen the long-term occupied space (space absorption) in accordance with economic theory. Available stock can be forecasted by past rent and absorption levels owing to the developer's profit-driven nature.

An understanding of the interaction between the macroeconomic variables and the Central Area office market is useful to domestic and foreign investors and developers, who then can better evaluate their decision making in commercial real estate investment and development projects.

It is implicit that the Singapore Central Area office market requires at least a year before any rental increase can potentially dampen the space demanded. Firms are attracted to locate there owing to agglomeration economies and they are willing to pay premium office rents in conjunction with office space intensification in the Central Area. Newly built space is positively affected by past rents. Urban Redevelopment Authority and private real estate developers should be wary of excess office sector vacancies by avoiding over supply, even though an increase in the supply of office space in the Central Area can have a positive impact on office rent in the longer term. Most of the office space development would tend to meet the demand in the long run. Rental stickiness is exemplified as rental changes are affected by lagged rent.

Policy makers are better enabled to stabilize the office sectors of the real estate market if so required.

The paper adopts the VECM and validated by empirical evidence, to investigate the long-run equilibrium relationship and short-term corrections underlying the dynamics of the Singapore Central office market. Delay in the restoration of equilibrium in real estate markets is attributed to factors like lease terms and supply lags.

The paper's objectives are: to address the issue of cointegration (efficient market hypothesis) between Greek spot and futures markets over the period of the crisis, 1999‐2001; to investigate the short‐run and long‐run efficiency of the FTSE/ASE‐20 stock index futures contract and FTSE/ASE Mid 40 stock index futures contract traded on the Athens Derivatives Exchange (ADEX).

This paper examines efficiency of the Greek stock index futures market from 1999 to 2001. A variety of econometric models are employed to test for cointegration between prices. The paper uses daily data from the Athens Stock Exchanges (ASEs) and the ADEX. A more detailed discussion on the causal relationship between spot and futures price in ADEX is obtained by using the impulse response functions of the vector error‐correction model (to study the behaviour of series from real shocks).

The results show that the Greek futures and spot prices form a stable long‐run relationship. For both FTSE/ASE‐20 and FTSE/ASE Mid 40, futures markets play a price discovery role, implying that futures prices contain useful information about spot prices. Futures markets are informationally more efficient than underlying stock markets in Greece.

The results have important implications for both traders and speculators. The findings are strongly recommended to financial managers dealing with Greek stock index futures.

The contribution of this paper is to provide evidence using data from the early stage of the ADEX (started its official operation on 27 August 1999). It also investigates whether the hypotheses exist after the dramatic rise of ASE stock prices.

This paper aims to investigate the causal nexus between foreign direct investment (FDI) and economic growth in SAARC countries.

Johansen's cointegration test was employed to examine the long‐run relationship between foreign direct investment and economic growth in SAARC countries. Besides, the vector error correction model (VECM) was employed to examine the causal nexus between foreign direct investment and economic growth in SAARC countries for the years 1970‐2007. Finally, the impulse response function (IRF) has been employed to investigate the time paths of log of foreign direct investment (LFDI) in response to one‐unit shock to the log of gross domestic product (LGDP) and vice versa.

The Johansen cointegration result establishes a long‐run relationship between foreign direct investment and gross domestic product (GDP) for the sample of SAARC nations, namely, Bangladesh, India, Maldives, Nepal, Pakistan and Sri Lanka. The empirical results of the vector error correction model exhibit a long‐run bidirectional causal link between GDP and FDI for the selected SAARC nations except India. The test results show that there is a one‐way long‐run causal link from GDP to FDI for India.

This paper employed annual data to examine the causal nexus between FDI and economic growth. Therefore, researchers are encouraged to test the FDI‐growth relationship further by using quarterly data.

The SAARC nations should adopt effective policy measures that would substantially enlarge and diversify their economic base, improve local skills and build up a stock of human capital recourses capabilities, enhance economic stability and liberalise their market in order to attract as well as benefit from long‐term FDI inflows.

This paper would be immensely helpful to the policy makers of SAARC countries to plan their FDI policies in a way that would enhance growth and development of their respective economies.