Overview of Economic Forecasting Methods

Overview of Economic Forecasting Methods:

Forecasting Techniques

Causal Time Series Qualitative Methods Methods Methods

Regression Moving Delphi Analysis Average Method

Multiple Exponential Jury of Regression Smoothing Executive Opinion

Trend & Sales Force Seasonal Qualitative Composite Decomposition Regression Logit, Probit Box-Jenkins Consumer ARIMA Market Survey

1 a. Causal (Multivariate) Forecasting Methods: Regression methods Make projections of the future by modeling the causal relationship between a series and other series. Can use time series or cross-sectional data to forecast.

Yt = f (Xt)

or Yt = f (X1t, .., Xkt, Y2t, ..,Y1k)

Methods: Simple or Multiple models Systemequation models Seeming unrelated models b. Univariate forecasting methods or Time series methods Using the past, internal patterns in data to forecast the future.

Yt+1 = f (Yt, Yt-1, Yt-2, Yt-3)

Methods: Moving average Smoothing and Exponential smoothing Decomposition: Seasonal and trend decomposition ARIMA(box-Jenkins) c. Multivariate Time series methods

Y1t = f (Y1,t-1, .., Y2,t, …,Yj,t, .., X1,t,…, Xj,t-k)

Methods: Multivariate ARIMA models Autoregressive and distributed-lag models Vector Autoregression (VAR) Vector Error Correction (VEC) models ARCHand GARCH models d. Qualitative Forecasting Methods: Dummy variables are used to characterize the information that choices are involved. Such data is referred to as qualitative data. Models including yes-no-type as dependent variables are called dichotomous, or dummy dependent variable regression models. There are three approaches to estimating and forecasting such models; (1) Linear Probability model (LPM), (2) Logit model, (3) Probit model and Tobit model.

Other qualitative forecasting methods are based on the judgement and opinions of others, such as concerning future trends, tastes and technological changes. Qualitative methods include Delphi, market research, panel consensus, scenario analysis, and historical analogy methods of predicting the future. Qualitative methods are useful when there is little data to support quantitative methods.

2 Understanding the classifications of economic data:

1. Primary versus secondary data: The first hand data are called primary data: In natural sciences, the bulk of data are generated by running experiments in a laboratory under a controlled environment in which factors are determined by the researchers according to their theoretical design. Therefore, the quality of data is very often control by the researchers.

In social sciences, particular in economics, researchers cannot create their own data by running experiments in a laboratory. They must rely on the data collected by official or agencies. Data collected by another party are called secondary data. If the data do not meet the desired standard of quality, social scientists cannot afford to throw them away. Instead, they must patiently and carefully treat or adjust these data by means of different econometrics and statistical methods.

2. Time-Series versus cross-sectional data Time series is a collection of observations generated sequentially through time. Time series data can be observed at many "frequencies". The common frequencies of economic data are annual, quarterly, monthly, weekly, and daily. The minute-by-minute and even the second-by-second data are also very commonly used in the financial researches.

Cross-sectional data are observations generated from different economic units in a given time period. These units might refer to firms, factors, groups, people, areas, provinces, regions, or countries, etc.

Panel (or pooled) data combines the time-series and cross-sectional approaches.

3. Macroeconomic versus microeconomic data Highly aggregated data that measure the activity in the economy as a whole, such as GDP, implicit price deflator, interest rate, unemployment rate, money supply, etc., are called macroeconomic data.

Disaggregated data that measures the economic activity of an individual household, factor, firm, or industry are called microeconomic data.

4. High-frequency versus low-frequency data Most economic data are collected over a discrete interval of time. The length of the discrete interval classifies measurements into annual, semiannual, quarterly, monthly, weekly, or daily data. Data collected over longer intervals are released less frequently, this type of data is called low-frequency data. Hourly, daily or weekly data is called more high-frequency data. Real-time data is the data reflect events at the moments, all others are called historical data.

5. Quantitative versus qualitative data The economic data have a number corresponding to each economic unit, described as previous data sets, is referred to as quantitative data. When we want to characterize a series of information such "yes" or "no", "good" or "bad", "male" or female", or others. These data information is referred to qualitative data. Such data arise often in economics when choices are involved. When we convert these qualitative

3 characteristics into numeric data, we might assign 1 = "yes" and 0 = "no". When a variable take on only the numeric values 1 and zero, they are referred to as dummy (or binary) variables.

Measurement and conversion of economic data

1. Economic variable measured as levels

Flow variable: data flows overtime as a stream. Stock variable: a measurement at a particular point of time and is the accumulation of all past flows. For example, investment in a given year is a flow variable, and the capital stock is a stock variable.

2. Economic variables measured as indexes Index is the series data based on a particular based period (notation with subscription 0) or reference period, the levels of the variable in other time periods (notation with subscript with t) are compared with the based-period level and measured. An economic indicator measured as an index must have a known base period to show relative magnitude. Without a base period, the index itself is not meaningful. There are two example types of price indexes

Laspeyres index of t period = 100*¦PtQ0 /¦ P0Q0 (Base-weighted index)

Paasche index of t period = 100*¦PtQt /¦ P0Qt (Current-weighted index)

Effective exchange rate index = ¦wiEi (Where wi is the weight)

Real exchange rate index = E(HK$/US$) x (US Price index/ HK Price index)

Others such as production index, and wage index, etc are measured in index.

3. Economic variables measures as growth rates and ratios Economic variables measured in term of percentage change or ratios are derived from level or index variable. For examples:

Growth rate = 100*(GDPt – GDPt-1)/GDPt-1

Inflation rate = 100* (CPIt – CPIt-1)CPIt-1

Unemployment rate = 100* (Labor force – Employment)/Labor force

Exchange rate = Domestic currency (units value)/ foreign currency (unit value)

In many instances, management finds forecasted growth rate of an economic variables to be of more interest than forecast of absolute levels. Growth rate conversions tend to focus attention on marginal changes rather than absolute level. This type of transformation is specifically useful when we are developing forecasts with multiple economic variables measured in different units. For example: if we want to generate a forecast for interest rates (measured in

4 percentage term), one of the factors that we might consider would be the money supply (record in billions of dollars). Therefore, it is more useful to convert the money supply data to a percentage growth format similar with the interest rates.

4. Linear Transformation Linear transformations are specifically useful when applying regression analysis to forecasting problems. Specifically, regression analysis begins by assuming that the relationship between variables is linear. The advantage of this type of conversion is that we have been able to take a relationship that does not satisfy the requirements of linearity and transform the data. The two common methods are:

- logarithmic transformation

- square root transformation

Eight Steps of Forecasting

1. Determine the use of the forecast – what objective are you trying to obtain? 2. Select the items or quantities that are to be forecasted. 3. Determine the time horizon of the forecast – is it short term (1-30 days), medium term (one month to one year), or long term (more than one year). 4. Select the forecasting method or model(s). 5. Gather the data needed to make the forecast 6. Validate the forecasting model 7. Make the forecast. 8. Implement the results.

5 Understand the common patterns of Time series: When a time series is plotted, common patterns are frequently found. These patterns might be explained by many possible cause-and-effect relationships.

Random patterns: Random time series are the result of many influences that act independently to yield nonsystematic and non-repeating patterns about some average value. Purely random series have a constant mean and no systematic patterns. Simply averaging model are often the most best and accurate way to forecast them.

time

Trend patterns: A trend is a general increase or decrease in a time series that lasts for approximately seven or more periods. A trend can be a period-to-period increase or decrease that follows as a straight-line, this kind of pattern is called a linear trend. Trends are not necessarily linear because there are a large number of nonlinear causal influences that yield nonlinear series. Trends may cause by long-term factors or population changes, growth during production and technology introductions, changes in economic conditions, and so on.

Y Y

Time Time

6 Seasonal Patterns: Seasonal series result from events that are periodic and recurrent (e.g., monthly, quarterly, changes recurring each year). Common seasonal influences are climate, human habits, holidays, repeating promotions, and so on.

Time Q1 Q3 Q1 Q3 Q1 Q3

Cyclical Patterns: Economic and business expansions and contractions are most frequent cause of cyclical influences on time series. These influences most often last for two to five years and recur, but with no known period. In the search for explanation of cyclical movements, many theories have been proposed, including sunspots, positions of planets, stars, long wave movements in weather conditions, population life cycles, the growth and decay cycle of new products and technologies, product life cycles, and the economic cycles. Cyclical influences are difficult to forecast because they are recurrent but not periodic.

Time

Autocorrelated Patterns: Correlation measures the degree of dependence or association between two variables. The Term autocorrelation means that the value of a series in one time period is related to the value of itself in previous periods. With autocorrelation, there is an automatic correlation between observations in a series.

Y Y

Time Time

7 Outliers: The analysis of past data can be made very complex when the included values are not typical of the past or future. These non-typical values are called outliers, which are very large or small observations that are not indicative of repeating past or future patterns. Outliers occur because of unusual events.

Time

The importance of Pattern:

One of the fundamental assumptions of most univariate forecasting methods is that an actual value consists of one (or more) pattern plus error. That is,

Actual Value = Pattern(s) + Error

When the pattern of the actual value is a repeating pattern, this behavior can be used to predict the future value. We describe past patterns statistically. Therefore, the first step in modeling a series is to plot it versus time and reveals it statistics.

Basic Tools in forecasting: In forecasting context, statistically analysis is used to extract information from the past. Based on more accurate forecasts, more effective decisions are possible, thus

Raw data Æ information (i.e., pattern) Æ forecasts Æ decisions

1. Graphs and bar charts z Time plot graphs z Histograms z X-Y scatter plots z Others

2. Probability estimations: a. Probability estimates using past percentage frequencies i.e. probability distribution

8 b. Probability estimates using theoretical percentage frequencies i.e., theoretical properties c. Probability estimates using subjective judgment i.e., decision maker’s subjective estimation

3. Univariate summary statistics: Comparisons of measures and the properties of central values: Mean: The statistical term for average Standard deviation (SD): Interpreted in a comparative sense. Median and Mode: Measures of the center location of a distribution.

4. Measuring Errors: Error = Actual – Forecast

Absolute Error Relative Error eˆ ¦ t (Y Yˆ ) ME t t PEt u100 n Yt eˆ PE MAD ¦ t MPE ¦ t n n PE SSE eˆ 2 MAPE ¦ t ¦t n eˆ 2 eˆ 2 MSE ¦ t RSE ¦ t n n1

Statistically Significance Test for Bias

Ho: et 0

H1: et z 0

The simple t-test can be used to determine how many standard errors of the mean error that is away from the hypothetical mean of zero.

e 0 t * calculated t Se / n

Where Se is the standard deviation of errors about its mean et , and (e e ) 2 Se ¦ t t n 1 Decision rule:

If | t* | d tc, no statistically significant bias has been found. If | t* | > tc, there is statistically significant bias.

Understanding correlation Predictive ability is achieved when it can be shown that the values of one variable move together with values of another variable. While the positive and negative are attributes of a relationship, however, they do not denote the strength or degree of association between each variable. Therefore, other measures such as covariance, correlation, auto-covariance and auto-correlation coefficients can be used for identifying and diagnosing forecasting relationship.

Correlation Measures: (Pearson correlation coefficient) Let X and Y be two variables and suppose the data have N observation such as i = 1 to N.

The correlation between X and Y is denoted by a small letter, rxy, and is calculated by the follow formula:

¦(Yi Y )(X i X ) rxy 2 2 ¦(Yi Y ) (X i X ) (X X )(Y Y ) Covariance: Cov(X ,Y ) ¦ i i n 1

The covariance is the mean of the product of the deviations of two numbers from their respective means. The correlation coefficient measures the proportion of the covariation of X and Y to the product of their standard deviations.

Cov(X ,Y) Therefore, rxy S xSY

The properties of correlation: 1. The r always lies between -1 and 1, which may be written as -1d r d 1. 2. If r = -1, there is a perfect negative relationship; if r = 0, there is no relationship; If r = 1, there is perfect positive relationship. 3. The correlation between X and Y is the same as the correlation between Y and X. 4. The correlation between any variable and itself is always equal 1.

Correlation does not necessarily imply causality:

It is widely accepted that cigarette smoking causes lung cancer. Suppose we have collected data from a group of people on (a) the number of cigarettes each person smokes per week (X) and (b) on whether they have ever had or now have lung cancer (Y). Since we have undoubted that smoking causes cancer and find rxy > 0. The positive correlation means that people who smoked tend to have higher rates of lung cancer than non-smokers. Here the positive correlation between X and Y indicates direct causality.

Now suppose that we also collect data on the same group of people to measure the amount of alcohol they drink in a typical week. Suppose we assign this new variable as Z. In practice, it is the case that heavy drinkers also tend to smoke and hence, rxz > 0. This correlation does not mean that cigarette smoking also cause people to drink.

10 Rather it probably reflects some underlying social attitudes. It may reflect the fact, in other words, that people who smoke do not worry about their nutrition, or that their social lives revolve around the pub, where drinking and smoking often go hand in hand. In either case, the positive correlation between smoking and drinking probably reflects some underlying causes (e.g. social attitude) which in turn causes both. Thus, a correlation between two variables does not necessarily mean that one cause the other. It may be the case that an underlying third variable is responsible.

Now consider the correlation between lung cancer and heavy drinking. Since people who smoke tend to get lung cancer more, and people who smoke also tend to drink more, it is not unreasonable to expect that lung cancer rates will be higher among heavy drinkers (i.e. rxz >0). Note that this positive correlation does not imply that alcohol consumption causes lung cancer. Rather, it is cigarette smoking that causes cancer, but smoking and drinking are related to some underlying social attitude. This example serves to indicate the kind of complicated pattern of causality which occurs in practice, and how care must be taken when trying to relate the concepts of correlation and causality. The general message that correlation can be very suggestive, but it cannot on its own establish causality.