The ftinaion LinearRegSlope ves the one-peiiod increase or decrease in the value based on a straight line fit of the past n days, and can be added to the current value to get the one-day-ahead forecast. The period can be selected by subtracting the actual next-day value from the forecast and creating an error series that can be measured using a standard deviation. The number of days, n, that generates the smallest standard deviation ts tbe best forecast period. It is likely that the optimal forecast period will differ for each of the four items above, and this becomes a matter of concem. is there a reason why the forecast period be the same for all of the predictions? If we are independently trying to forecast volume, then fixing the periods at the same length does not seem necessary, if we are trying CO discover wliether a change in volume is related a change in price as we are here, then the same regression Interval seems important. (These and other testing procedures are thoroughly discussed in Chapter 21 ("Testing").

Having found the four one-day-ahead forecasts, an index can be created that ves one weight ivi to the price forecast and the balance, 1 - »!, to a combination of the other three factors. This assumes that price is the most important predictor of price.

Forecast Index = ;, x Pf + (1 - ;,) x (MaVf + MjOf + M;40BVf)

This formula can be backtested for values of i ,, /z, w, and »* between 0 and I. The final index can be used instead of price for determining the trend. It will still require a moving average, or some trendline, to signal new uptrends and downtrends; however, the results, if successful, should be more reliable than only using price.

One advantage of testir the weighting factors is that, if one of the four elements is not helfl in predicting a trend, the weighting factor should be zero. Another approach, that does not cluster the nonprice data together, would be to treat each item separately:

Forecast Index = tt,Pf -I- ttjVf -I- wOi + wOBVf

and where 2 "i = 1

The sum of the weighting factors should alwajs be 1, equalto 100° o. INTRADAY VOLUME PATTERNS

Identifjing increases and decreases in volume during the trading day must consider overriding pattems caused by the way traders enter orders. The pattem of intraday volume can be seen using tick volume as a practical substitute for actual volume, which is usually not available until the next day. To create a meanful chart of 30-minute volume pattems, each interval was compared with the first 30 minutes of the day and recorded as a percentage of that initial tick volume. Figure 10-2 shows the results of three futures maitets. Eurodollars, S&P 500, and Deutschemarks taken over a 1-year period using the nearest delivery.

The pattems of the three markets shown in Figure 10-2 are similar in that the greatest volume is at the beginning and end of the trading day, yet very different in their internal pattems. Eurodollars, which have the highesl volume of all futures maitets, show much larger volume on the opening and closing 30minute periods.

It should not be su rising to see the extreme clustering at both ends of the trading day. Orders enter the maitet early in reaction to news and events that occurred since the close of the previous days trading. There are also orders resulting fran trading decisions based on the previous days data but calculated after the close. The end of day is active

FIGURE 10-2 Pattems of 30-minute tick volume, 1993. (a) Eurodollars, (b) S&P 500. to Deutschemaits.

FIGURE 10-2 (Continued)

¹,v,l,„d,nBll™(»lVt

because of juggling for position based on todays price movements. For most traders, the closing price is the most dependable value of the day.

There is a tjpical rounded bottom formation on most charts, with lowest volume in the late morning when traders take their breaks. Deutsche marts (Figure 10-2c) differ from the others by showing more sustained high volume through late moming. This is because the European markets are open during that period. London interbank markets are likely to be open at 5 P.m. (12 noon in New York), to overiap U.S. trading as much as possible. Volume on the IMM Deutschemait contract tapers off after European business hours end.

When trading based on an increase in volume, these pattems must serve as the norm. To decide whether there is a volume confirmation for a trade to be entered at 11 A JVI., YOU must compare todays 30-minute volume for the 11 A.M. interval with the previous average volume for this same period only. This is equivalent to deseasonalizing or dehending the data. Even with this precaution, an increase in volume for a thinly traded market, such as cocoa, may appear significant because the 30minute volume jumped from 100 contracts to 300 contracts during midday. This can easily be misleading. You will need to consider the sample error in low-volume markets or demand much larger volume changes to be more certain.

FILTERING LOW VOLUME

It seems clear that minutes, hours, or even days that have litUe maitet activity are likely to be associated with uncertain price direction. If the British pound moves the equivalent of $.50 in the early afternoon of the U.S. market, we know that volume is normally light and the London and European markets are closed. If the intention of a volume

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indicator is to identifj positive moves in volume tliat can be used as a confirmation of price direction, then eliminating those dajs with low volume, or with marginal price moves, may make the volume indicator dependable.

Removing Low-Volume Periods

The inclusion of low-volume periods into a volume index may make the index movements unreliable. There is a similar situation in statiatics, where a number of statiatical values are slightly skewed to one side. Each value on its own is not noticeably important, but collectively they cause a bias. Some analjsis believe that the collective weight creates a significant situation, while others favor ignoring any statistic that is too close to the norm to be distinguished When you ignore the individual values, there is no collective value. In the same way, by ignoring dsjs with lov\? volume, you do not have to rid; the chance of posting a series of dsys, all of which may be uncertain, that result in a confirmation of a new price direction. Dajs may be filtered if the volume falls one standard deviation below the average (removing 16°o of the total dsjs), or two standard deviations (removing only l.So of the dsjs), or any other combination. The use of absolute volume numbers, such as a dsy on the New York Stock Exchange with volume under 200 million, will not allow consistent filtering over any prolonged test. Then, on any dsy, the Volume-Filtered On-Balance Volume would be found by the following program or spreaddieet steps:

volume threshold @AVG(volurre, n) + f*@STD{volunie - volumeCl], n) if volume < volume threshold then VFOBV = VFOBV[I]

else VFOBV = VFOBVCl] + ((close - cl ose[ 1]) / (®ARS{close - closed])) * volume

where n is the number of periods in the average and standard deviation

f is the number of standard deviations used to filter minimum volume

Removing Volume Associated with Small Price Moves

Indicators such as On-Balance Volume post all volume as either a positive or negative contribution to the index, based on the direction of prices on that dsy. It is fair to question the validity of posting all volume to the upside when the S&P 500 closed up a minimum move of one-twentieth of one point (+.05). It could just as easily have closed down that amount. In a manner similar to filtering lowvolume periods, in the section above, periods in which prices moved very little may be eliminated by using a standard deviation of the price changes as a filter. Dajs which are within ±. 5 or ± 1.0 standard deviations of the average would be ignored The Price-Filtered On-Balance Volume would then be found as follows:

pr1ce thresnold = @AVG(price - priceCl], n) + f*@STD{pr1ce - priced],n) if @ABS{price - price[l]) < pricG threshold then PFOBV = PFDBV[1]

else PFOBV = PFOBVCl] + ((close - closeCl] )/(@ABS{close - closed])) * volume

wtiere n is the number of periods in the average and standard deviation

f is the number of standard deviations used to filter minimum volume

Note that, m the case of a mmimum price threshold, the rules look at price change, which can be positive or negative. For a volume threshold there is only a one-sided test.

MARKET FACILITATION INDEX

In weighing the likelihood that prices are indicating a direction, rather than a false start, the tick volume compared with the price range for the same period, called the Maiket Facilitation Index, can measure the willingness of the maiket to move the price. This concept is interesting because it is not clear that high volume results in a laige price move, although it sppears to set up the conditions for high volatility if the Maiket Facilitation Index increases, then the maiket is willing to move the price; therefore, trading profits are more likely.

Bill WiUianiE Tra.W:baoE(J..Uu Wiley frcons 19951