Residual-based test for Nonlinear Cointegration with application in PPPs

Nested by linear cointegration first provided in Granger (1981), the definition of nonlinear cointegration is presented in this paper. Sequentially, a nonlinear cointegrated economic system is introduced. What we mainly study is testing no nonlinear cointegration against nonlinear cointegration by residual-based test, which is ready for detecting stochastic trend in nonlinear autoregression models. We construct cointegrating regression along with smooth transition components from smooth transition autoregression model. Some properties are analyzed and discussed during the estimation procedure for cointegrating regression, including description of transition variable. Autoregression of order one is considered as the model of estimated residuals for residual-based test, from which the teststatistic is obtained. Critical values and asymptotic distribution of the test statistic that we request for different cointegrating regressions with different sample sizes are derived based on Monte Carlo simulation. The proposed theoretical methods and models are illustrated by an empirical example, comparing the results with linear cointegration application in Hamilton (1994). It is concluded that there exists nonlinear cointegration in our system in the final results.

Elbesparing med pelletkaminer och solvärme i direktelvärmda småhus

The aim of this study was to investigate how electricallyheated houses can be converted to using wood pellet and solarheating. There are a large number of wood pellet stoves on themarket. Many stoves have a water jacket, which gives anopportunity to distribute the heat to domestic hot water and aradiator heating system. Three typical Swedish houses with electric resistanceheating have been studied. Fourteen different system conceptsusing wood pellet stoves and solar heating systems have beenevaluated. The systems and the houses have been simulated indetail using TRNSYS. The houses have been divided in up to 10different zones and heat transfer by air circulation throughdoorways and open doors have been simulated. The pellet stoveswere simulated using a recently developed TRNSYS component,which models the start- and stop phases, emissions and thedynamic behaviour of the stoves. The model also calculates theCO-emissions. Simulations were made with one stove without awater jacket and two stoves with different fractions of thegenerated heat distributed in the water circuit. Simulations show that the electricity savings using a pelletstove are greatly affected by the house plan, the systemchoice, if the internal doors are open or closed and thedesired level of comfort. Installing a stove with awater-jacket connected to a radiator system and a hot waterstorage has the advantage that heat can be transferred todomestic hot water and be distributed to other rooms. Suchsystems lead to greater electricity savings, especially inhouses having a traditional layout. It was found that not allrooms needed radiators and that it was more effective in mostcases t use a stove with a higher fraction of the heatdistributed by the water circuit. The economic investigation shows that installing a woodpellet stove without a water jacket gives the lowest totalenergy- and capital costs in the house with an open plan (fortoday's energy prices and the simulated comfort criteria). Inthe houses with a traditional layout a pellet stove givesslightly higher costs than the reference house having onlyelectrical resistance heating due to the fact that less heatingcan be replaced. The concepts including stoves with a waterjacket all give higher costs than the reference system, but theconcept closest to be economical is a system with a bufferstore, a stove with a high fraction of the heat distributed bythe water circuit, a new water radiator heating system and asolar collector. Losses from stoves can be divided into: flue gas lossesincluding leakage air flow when the stove is not in operation;losses during start and stop phases; and losses due to a highair factor. An increased efficiency of the stoves is importantboth from a private economical point of view, but also from theperspective that there can be a lack of bio fuel in the nearfuture also in Sweden. From this point of view it is alsoimportant to utilize as much solar heat as possible. Theutilization of solar heat is low in the simulated systems,depending on the lack of space for a large buffer store. The simulations have shown that the annual efficiency ismuch lower that the nominal efficiency at full power. Thesimulations have also shown that changing the control principlefor the stove can improve efficiency and reduce theCO-emissions. Today's most common control principle for stovesis the on/off control, which results in many starts and stopsand thereby high CO-emissions. A more advanced control varyingthe heating rate from maximum to minimum to keep a constantroom temperature reduces the number of starts and stops andthereby the emissions. Also the efficiency can be higher withsuch a control, and the room temperature will be kept at a moreconstant temperature providing a higher comfort.

Testing common nonlinear features in vector nonlinear autoregressive models

This paper studies a special class of vector smooth-transition autoregressive (VSTAR) models that contains common nonlinear features (CNFs), for which we proposed a triangular representation and developed a procedure of testing CNFs in a VSTAR model. We first test a unit root against a stable STAR process for each individual time series and then examine whether CNFs exist in the system by Lagrange Multiplier (LM) test if unit root is rejected in the first step. The LM test has standard Chi-squared asymptotic distribution. The critical values of our unit root tests and small-sample properties of the F form of our LM test are studied by Monte Carlo simulations. We illustrate how to test and model CNFs using the monthly growth of consumption and income data of United States (1985:1 to 2011:11).

Forecasting with Vector Nonlinear Time Series Models

This work concerns forecasting with vector nonlinear time series models when errorsare correlated. Point forecasts are numerically obtained using bootstrap methods andillustrated by two examples. Evaluation concentrates on studying forecast equality andencompassing. Nonlinear impulse responses are further considered and graphically sum-marized by highest density region. Finally, two macroeconomic data sets are used toillustrate our work. The forecasts from linear or nonlinear model could contribute usefulinformation absent in the forecasts form the other model.

Residual-based Inference for Common Nonlinear Features

This paper investigates common nonlinear features in multivariate nonlinear autore-gressive models via testing the estimated residuals. A Wald-type test is proposed and itis asymptotically Chi-squared distributed. Simulation studies are given to examine thefinite-sample properties of the proposed test.