By analyzing the graphical representation of the Housing starts and completions data, we can rest assured of no presence of trends except for a minor downward trend towards the end that can be ignored.
Moreover, we should not allow for trend in the Housing starts and completions model, because regressing both trends against each other will be similar to regressing time against time, which will lead to highly unrealistic positive values in terms of R squared and t-statistics. If the data are trending, then it should be de-trended by taking the residual of each series and then using them in the regression model.
By excluding the lags of completions from the starts equation, we obtain the below results from EViews, which do not differ significantly from the results of the starts VAR model except for a better accuracy statistics. The compared results are:
The SIC and BIC statistics are lower in the Univariate model predicting more accuracy and it is also reasonable since both statistics favor the most parsimonious model. In addition, observing the graph of the estimation along with the residual, we can notice a random error with zero mean on average and a closely fitted estimation over the actual data.
Comparing the univariate models of starts with the VAR model of starts with lags of completions, we can observe a more accurate forecast graph of univariate forecast.
We should expect to see low values of R squared, t-statistics and F-statistics since these tools indicate how much the dependent variable is explained by the independent variable. Therefore, since y and x are unrelated we should expect to see low values of each of the statistical tool revealing that the variables do not explain each other.
Regressing y against x will yield high values of R squared, t and F statistics indicating high correlation between the variables. This is normal for the fact that both variable tend to follow each other and present a flaw strong regression model. Since the regression is spurious we should expect to find a third variable that influence both x and y. Hence, it is misleading to follow the large statistical values of the regression.
Moreover, we tend to find a very low Durbin-Watson statistic, which is a test for first-order serial correlation in the residuals of a time series regression. Small values of the Durbin-Watson statistic signify the presence of high serial residual autocorrelation.
The Durbin-Watson statistic should be viewed as a warning of a spurious relationship.
To insure against spurious regression in case x does not explain the dependent variable, then modeling the dynamics in y would be a proper solution. Moreover using lagged dependent variables also would also be another solution in which these models get at the idea that yt follows an autoregressive process but that xt is a series of shocks, driving y to new levels. Durbin Watson statistic or even Durbin's h can be used to detect any presence of spurious regression.
There are many methods out there that are used for asset valuations such as the Capital Asset Pricing Model (CAPM), Discounted Cash Flows (DCF), and the Dividend Yield (DY). All of those methods have proven to have substantial validity in the field of finance. Those methods are used to estimate the current value of a tangible asset (stock, bond, and factory) or an intangible asset (patent, copyright, and goodwill). They are considered to be the basis that is used for the estimation of the future value of those assets.
There are many quantitative and qualitative factors that affect the values of stocks, bonds and interest rates. Some of the quantitative factors are the asset's book value, market value, and historical prices. Depending on the availability and quality of the needed data, we could undertake an autoregressive model (or other long term forecasting methods) and compare the performance achieved with a random walk.
The spot price of any security is known as the immediate deal price for that security in the relevant market. The idea of having the future spot price of any security involves so many factors such as, economic conditions, the demand of the security in question, both national & international, the historical prices of the security, the historical trends of the security, the historical cycles of the industry, and most importantly the judgments and assumptions of the people who are doing the forecasts.
Exchange rates are nothing but the price for currencies. They increase and decrease depends on the international demand of the currency. It is usually calculated using a base or home currency (Usually the USD) and a foreign currency. It measures for example, how many Dirhams can be bought using 1 US dollar. There are many factors that are taken into consideration when undergoing a forward exchange rate forecast such as economical, political, and legal factors, to name a few. Those are all very complex factors in nature and cannot be easily forecasted by relying only on historical quantitative components; there are many other qualitative components that contribute to the overall economy.
Based on the above mentioned, we believe that the forward exchange rates do have some bias factor in providing forecasts of future spot rates. We believe that the forecast residual (known as the difference between the forecasted and actual values) will not have a zero mean at all horizons, especially that there is a lot of subjectivity from the analysts represented through their own judgment and assumptions involved in the forecast. It is worth mentioning though that if we observed a forecast residual mean that is statistically equal to zero, then it will be safe to say that the forecasting model is unbiased.
Government budgets can be seen as a 4-step process - formulation, solution, justification, and implementation (Larkey and Smith, 1989). Formulation is the process whereby the budgeters will assess where they are now, and where they want to be. This will allow them to specify how they want to get from here to there. Solution is the process where they will setup a set of tasks to reach the intended destination. Justification is the method used by budgeters to convince others of their solution and formulation techniques. Implementation is reached once the budget is communicated to all stakeholders and the needed directives are undertaken to reach the desired result. Any deviation in a budget, over or underestimating, will be a result of a deviation in any of these four steps.
In governments, budgeters have a huge incentive to overstate their budgets. First of all, the general population interprets a deficit as a negative sign that is resulted from bad management and bad governing. If a surplus is reached then the public will analyze this as a great achievement of the people in charge and the finance people in the government. Secondly, having a surplus will release any administrative pressure on the executives. This is especially true across departments since they won't have to cut any departmental spending due to a deficit. This gives the executive more control over the finances since they won't be limited to a deficit budget. Furthermore, a public hearing is needed for the allocation of the annual budget but not for any amendments made. Therefore, executives can announce an optimistic budget but later adjust it to realty without any public problems.
Based on the findings of Hafer and Hein (1990), we can use nominal interest rates to forecast future inflation by applying the Fisher equation. However, it is better to start with a time series forecast of inflation first (such as autoregression) and then use interest-rate-based forecasts of inflation to enhance the model by checking if including lagged interest rates provides incremental predictive enhancements.
The essence of using judgment is to basically add information to a forecast that a model cannot include. An analyst could be aware of certain changes in the environment like policy changes or others that will affect the results. To incorporate these variables in a model would be difficult. Instead, they are added to the model results as expert judgment. The most important factor to ensure that judgments are useful is to make sure that they include information that cannot be collected by the forecasting model. A forecast basically uses past information to come up with forecasts and predictions of the future. It is ideas about current issues or pending topics that will be incorporated into a model as judgment. But, the use of judgment is biased by the individual's motives. If the results of a forecast were to alter certain decisions, a person would be motivated to provide judgment that could affect these judgments.
When one includes qualitative judgment into a forecasting process, you generally affect the quantitative results that are obtained. There are three basic methods by which judgment can be included. The first approach is by aggregating the forecasts and predictions of any front-line individuals that deal with the real-time data. They will be able to include what data is relevant to the forecast. The second way to add judgment is to simply include any expert consensus on the issue. They will be able to adjust the forecast models towards the appropriate approach to be used. The third method is to partake in the Delphi Technique whereby these experts are interviewed one by one and their recommendations or judgments are aggregated. These judgments are free from any group pressure due to them being performed one by one and they could lead to some sort of consensus. This information collected will add to the forecast time-sensitive information that could not be included in the model.
Judgment used in forecasting could be divided into informal and formal methods. Informally, one would include judgment is a presentation or meeting context. The individual expert would include their own insight into the results achieved from the forecasting process. Formally, a judgment can be included in a quantitative forecast by combining these expert ideas with the model-based forecasts that are performed using a forecast combination. Another formal method would be to simply skew the results towards an idea or viewpoint that is agreed upon using shrinkage. This change in the results wouldn't be in the matter of cheating the results. It should be agreed upon that the results are derived by applying some degree of freedom.
There are many procedures for including judgment. Armstrong and Collopy (1998) mentioned the following methods in the figure below:
Armstrong and Collopy further ad to their research a series of principles to ensure that the integration of judgment is successful:
- Judgment should be an input to forecasting and not independent or used as a revision tool
- Judgment and models should be equally weighted
- Judgment should be based on "now" information
- Revisions through judgment could harm the results if done by biased experts
- Armstrong, J. S. & Collopy, F. (1998). Integration of Statistical Methods and Judgment for Time Series Forecasting: Principles from Empirical Research. Retrieved on 14th November, 2009 from: http://mktg-sun.wharton.upenn.edu/ideas/pdf/integ.pdf
- Hafer, R. W. & Hein, S. E. (1990). Forecasting Inflation Using Interest-Rate and Time-Series Models: Some International Evidence. The Journal of Business, 63 (1), 1-17
- Larkey, P. D. & Smith, R. A. (1989). Bias in the Formulation of Local Government Budget Problems. Policy Sciences, 22 (2), 123-166