Estimated Standard Errors of CPI of Australia and US by Adding

Table A.2.3 Estimated standard errors of CPI of Australia by adding dummies

% Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4

1990 0.67 0.89 2000 1.01 0.93 0.91 0.67

1991 0.90 0.90 1.50 1.44 2001 0.61 0.55 0.56 0.87

1992 1.57 1.78 1.58 1.55 2002 0.68 0.74 0.57 0.41

1993 1.22 0.81 0.51 0.58 2003 0.43 0.65 0.68 0.75

1994 0.55 0.60 0.49 0.57 2004 0.91 0.67 0.51 0.66

1995 1.32 1.45 1.39 1.01 2005 0.66 0.53 0.57 0.43

1996 0.57 0.45 0.31 0.90 2006 0.60 1.01 0.99 0.87

1997 1.45 2.14 1.75 1.55 2007 0.53 0.57 0.82 0.87

1998 1.13 0.46 0.73 0.73 2008 0.84 0.84 0.75 1.11

1999 1.11 0.97 1.18 1.32 2009 1.41

Table A.2.4 Estimated standard errors of CPI of US by adding dummies

% Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nob Dec Ave

1990 0.44 0.34 0.18 0.18 0.31 0.27 0.16 0.30 0.23 0.51 0.63 0.68 0.35

1991 0.16 0.33 0.38 0.43 0.32 0.26 0.31 0.32 0.22 0.46 0.50 0.52 0.35

1992 0.30 0.09 0.14 0.30 0.33 0.39 0.43 0.31 0.14 0.10 0.13 0.12 0.23

1993 0.17 0.26 0.21 0.13 0.10 0.10 0.15 0.08 0.23 0.23 0.23 0.30 0.18

1994 0.27 0.28 0.23 0.21 0.31 0.30 0.32 0.32 0.30 0.25 0.24 0.32 0.28

1995 0.53 0.55 0.58 0.57 0.69 0.67 0.41 0.22 0.19 0.16 0.14 0.21 0.41

1996 0.15 0.26 0.25 0.18 0.20 0.28 0.26 0.23 0.18 0.25 0.28 0.41 0.24

1997 0.27 0.28 0.30 0.44 0.59 0.54 0.51 0.42 0.39 0.42 0.27 0.18 0.39

1998 0.12 0.11 0.10 0.09 0.07 0.08 0.14 0.10 0.10 0.09 0.07 0.16 0.10

1999 0.23 0.18 0.29 0.31 0.30 0.34 0.26 0.23 0.31 0.36 0.37 0.49 0.31

2000 0.45 0.56 0.86 0.38 0.36 0.69 0.42 0.19 0.29 0.34 0.35 0.39 0.44

2001 0.52 0.49 0.66 0.46 0.44 0.48 0.63 0.56 0.35 0.53 0.86 0.25 0.52

2002 0.12 0.14 0.22 0.33 0.17 0.24 0.60 0.73 0.30 0.37 0.27 0.28 0.31

2003 0.53 0.85 0.64 0.28 0.42 0.35 0.30 0.16 0.15 0.31 0.35 0.34 0.39

2004 0.36 0.37 0.41 0.33 0.41 0.38 0.25 0.23 0.25 0.41 0.67 0.57 0.39

2005 0.22 0.24 0.29 0.52 0.13 0.12 0.42 0.91 0.72 0.45 0.33 0.27 0.39

2006 0.52 0.37 0.24 0.41 0.72 0.66 0.61 0.36 1.27 0.62 0.76 0.41 0.58

2007 0.76 0.72 0.36 0.63 0.56 0.64 0.88 1.04 0.40 0.40 0.18 0.40 0.58

2008 0.23 0.21 0.76 0.59 0.56 0.13 0.21 0.40 0.33 0.62 1.14 1.83 0.58

Chapter 3. An Application of Henriksson-Merton Test: Are Fed Funds Rate Futures Valuable in Predicting US

Monetary Policy?

In this chapter, we apply the non-parametric generalized Henriksson-Merton (H-M) test proposed by Pesaran and Timmermann (1992, 1994) to verify the directional predictive ability of Federal Funds futures on Federal Funds rates.

I. Introduction

The Federal Reserve implements monetary policy by making discrete adjustments¹⁸ to its target for the Federal Funds (FF) rate. Changes in the FF rate triggers a chain of events that affect other short-term interest rates, foreign exchange rates, long-term interest rates, the volume of money and credit and, ultimately, a range of economic variables including employment, output and prices of goods and services. Therefore, how well markets anticipate the FF rate is a topic of great interest to financial market participants and policymakers alike¹⁹.

It is not surprising that a vast body of research have already studied the behavior of

Changes in the FF target rate are limited to multiples of 25 basis points since August 1989 (Poole and Rasche, 2003).

Although the Fed lowered the Fed Funds rate to 0~0.25% at 12/16/2008, giving up the Fed Funds rate

as an operation target of monetary policy and shifted to unconventional operation targets, as the US

economy bottoms and recovers, the Fed inevitably shall resume using the Fed Funds rate as operation

targets of monetary policy. Therefore, understanding the predictability of FF futures on Fed Funds rate

the FF rate and proposed empirical models designed to have it explained. The literature has suggested that several variables can explain FF rate movements: inflation and output gap (e.g. Taylor, 1993, Clarida, Gali, and Gertler, 1998, 2000), FF futures rates (e.g. Krueger and Kuttner, 1996, Robertston, and Thornton, 1997, Poole, and Rasche, 2000, Owen, and Webb, 2001, S¨oderstr¨om, 2001, Poole, and Rasche, 2003, Lange, Sack, and Whitesell, 2003) and other short or long term interest rate (e.g. Enders and Granger, 1998, Hansen and Seo, 2002, Sarno and Thornton, 2003, Clarida et al., 2006).

Among which, the FF futures rates were the most frequently used indicator to predict future FF rate movements, since its pricing information is widely available in a timely fashion while being recognized as essentially public and market-based forecasts of future interest rates of Federal Funds. The closing prices of each trading day are quoted on the financial pages of most major newspapers the next day. Moreover, real time quotes are available on the Internet with the CBOT’s website. Besides, the FF futures rates are better than the Treasury bond yields, another high frequency variable, as a predictor of monetary policy movement. Since the FF futures rates, unlike long and short term interest rates that are affected by other factors of demand (risk appetite) and supply (government deficit) in the market, the FF futures market is most affected by market expectation on future monetary policy.

Although vast many literature have studied the prediction power of FF futures rates on future FF rate movements, most research focus only on quantitative accuracy instead of qualitative (directional) accuracy. But changes in the FF target rate are discrete;

therefore a conventional quantitative accuracy test, such as MSE and MAPE based criterions, may not be a proper application. Furthermore, for most people, directional movement (raise, no change and cut) of the FF rate is important as well, since it

represents the FOMC’s tendency of monetary policy (tighten, neutral and ease). On the other hand, the U.S. monetary policy have became more “gradualism” (Lange, Sack and Whitesell, 2003) in late 1990’s, which means the monetary policy cycle of the US has become more obvious and prolonged since then. Therefore, the predicting power of the FF futures near the turning point of the monetary policy cycle is important as well.

In addition, market participants use the FF futures to foresee future U.S monetary policy as well, but few papers have discussed how many periods ahead are FF futures valuable in the sense of Henriksson and Merton (1981) in predicting future FF target rate movements²⁰. Furthermore, reviewing literature associated with FF futures, many papers have discussed the effects of the change in FOMC disclosure practice made at 1994/2, but qualitative measurements about this topic were rare.

Here we apply the non-parametric generalized Henriksson-Merton test proposed by Pesaran (1992) and Pesaran and Timmermann (1994) to fill these gaps in literature. The remainder of this chapter is organized as follows. In section 2, we briefly discuss some earlier studies about the prediction of FF rate by FF futures. In section 3, we introduce the Federal Futures market and illustrate how market participants use FF futures rates to anticipate the future FF rate. In section 4, we apply the generalized non-parametric

Henriksson and Merton (1981) applied Merton’s (1981) theory with Bayesian statistical methods to derive a test that could measure for the user whether the prediction for a variable by a model is meaningful and valuable. Straightforwardly, Merton’s (1981) argument could be summarized as follows:

Firstly, user of forecast (investors) may already have a prior view on a variable’s future value (expected

return on stocks). These views may be based on a combination of prior distribution. Secondly, after a

forecasting agency releases their forecast, the messages become part of the sample information collected

by the forecast user. Finally, after receiving these sample information, if the posterior distribution formed

by it may not only be different but also adjust to a more accurate direction than the aforementioned prior

Henriksson-Merton test on FF futures rates to predict future FF rates. The last section is concluding remarks.

II. A Review of Earlier Studies

A lot of literature has discussed the relationship between FF futures rates and the FF rate. We first review the rationality testing and forecasting accuracy evaluation, and then we discuss the importance of directional accuracy. Behavior of FF futures rates related to the monetary policy cycle and changes in the FOMC disclosure practice will then be discussed.

2.1. Rationality Testing and Forecasting Accuracy Evaluation

The first paper to examine the rationality of FF futures rates in explaining future FF rate movements is Krueger and Kutter (1996). They use monthly data from June, 1989 through November, 1994 by regressing the futures-based forecast errors (denoted as

t k t t k

f

⁺ −

r

) on a variety of economic indicators (denoted as

x

^t₋¹ ),

( ) 1 t k

t k t t k

f

t⁺ −

r

+ = +

a θ L x

− +

u

+ (1).

They found that the coefficients for economic indicators were rarely significant, which indicated that when information from futures is included, there may only be slight improvement, if at all, using economic indicators. Krueger and Kutter also examined the forecasting accuracy evaluation between futures based forecasts and

naïve²¹ forecasts by comparing out of sample forecasting MSE (MSFE).

Besides, Swason (2006) updated the sample period of earlier studies to include data since mid-2000 and found that despite a upswing in private sector forecast errors and uncertainty in 2001, an overall improvement in private sector interest rate forecasts with FF futures rate appears to be a robust feature of the data.

2.2. Importance of Directional Accuracy

Robertson and Thornton (1997) is the pioneer of directional accuracy on FF futures research studies. They used -9 and +21 basis points as the cut point to separate market expectation on the difference between futures rates and current target rate into two groups, —change and no change.²² They used hit ratio²³ as a measure of forecasting accuracy and found that the accuracy of one month ahead forecast is 70 percent.

However, their procedures are rough, since they did not consider the dates of FOMC meetings and they did not apply a formal test procedure.²⁴

The “naïve” forecast means forecaster would predict FOMC would always not change FF target rate in the future meetings. Krueger and Kuttner (1996) found that futures-rate-based forecasts are significantly more accurate than the “no change” forecast at one- and two-month horizons.

A spread between futures rate and current target rate that is outside the interval indicate an expected target change.

Hit ratio: the percentage of times that were accurately forecasted, which is the number of accurate forecasts divided by the number of total observations.

Although Hit Ratio is a numeric measure, it provides only an ordinal ranking of competing forecasts.

There is no way of knowing, from the Hit Ratio measure alone, whether a value of 0.68 is “good” or how

2.3. Monetary Policy Cycle

Carlson and McIntire (1995) found that predictive accuracy is the lowest around policy cycle turning points. Nosal (2001) found that futures rates on average over predicts the FF rate, and, over different phases of the business cycle, it may systematically over or under predict the eventual fed funds rates. Their research raises the question about the predictive power of FF futures around the turning points of the monetary cycle.

2.4 . Changes in FOMC Disclosure Practices

Poole and Rasche (2000, 2003) lead the study on effects of changes in FOMC’s disclosure practice by using daily frequency data to test the predictive power of FF futures rates on future FF rates. In their research, one-month-ahead FF futures rate changes were defined “large”, which represent surprise in monetary policy change, if a daily change in the futures rate exceeded five basis points. They found that the frequency of large changes in the futures rates have decreased over the decade, particularly after the February 1994 introduction of public announcements of changes in the intended funds rate at the conclusion of FOMC meetings. It indicates an improved understanding within the market of the information processed by the FOMC in reaching its policy decisions. Although their procedure was not delicate, their conclusions were of great value since they found that such institutional change can have huge impact on the transparency of monetary policy.

There was many advanced empirical research that shared Poole and Rasche (2000)’s spirits to test the predictive power of FF futures rates post 1994. Owens and Webb (2001) examined whether the forecast extracted from futures prices accurately

predicts the policy action thirty days later by estimating the following regression equation

30 30

( )

T f T

t t t t

i α β i

₋

i

₋

ε

Δ = + − + (2)

where

i is the FOMC’s target for the federal funds rate at the end of date t,

_t^T Δ is the difference operator,

i

_t^f₋₃₀ is the value of the federal funds rate target at date t anticipated by market participants thirty days earlier. Besides, they have also used probit analysis to estimate the following equation

Pr 30

T T

t t t

I i

Δ = +

α β

i

₋ + (3)

e

where

I i

Δ is an indicator variable that takes the value of one if the FOMC changes _t^T target rate in its meeting at date t, and zero if it chooses no change in target rate, PrΔ

i

_t^T₋30 is the implicit probability that the FOMC will change the federal funds rate target in the next thirty days. However, their data processing had a significant drawback, since the settlement price of FF futures rates is the daily average of effective federal funds rate. The time when FOMC meeting take place is important²⁵. Therefore, S¨oderstr¨om (2001) modified equation (2) of Owens and Webb (2001) as follows

1 ( ) 1

T e T

t t t t

i

₊

α β i i ε

₊

Δ = + − + (4)

Since settlement price of FF futures rate are average daily federal funds effective rate, one basis point

change on FF futures rate imply more propensity change on FF target rate when FOMC meeting take

place late of the month. Therefore, equal weighting on different FF futures rate inferring propensity of

where

i

is the futures-based funds rate expectation at date t considering the date of FOMC meeting take place.

III. Silent Features of the FF Future Rate

The 30-day Federal Funds Futures contracts started trading on the floor of the Chicago Board of Trade since October 3, 1988. The contracts are for the interest paid on overnight federal funds held for the contract month with a principal of $5 million and are priced on the basis of 100 minus the overnight federal funds rate for the delivery month. At maturity, the contract is compared with the daily average of effective FF rate as reported by the Federal Reserve Bank of New York. However, though FF futures are traded for the current month and for 23 future months, the effective contract is only about five months out (figure 3.1)²⁶.

Figure 3.1 1995~2007 Average FF futures Open Interests

0 10000 20000 30000 40000 50000 60000

1 2 3 4 5 6 7 8 9 10 11 12

Open Interests

Months to Deliver

Source: Bloomberg

Since average FF futures open interest exceed 10,000 only for 5 months out.

There are several studies about extracting the expectation of monetary policy from FF futures rates over time (S¨oderstr¨om, 2001, Owens and Webb, 2001, Sack, 2004).

Here we introduce the most commonly used procedure for extracting information from FF futures. Since there are four months of each year in which the FOMC doesn’t meet, the contract prices represent the expected federal funds target rate previously announced by the FOMC. Then, for each of the eight months in which the FOMC meets, calculating the expected FF rate is slightly more complicated. Since a FF futures rate is simply equal to the average of expected effective funds rate for the contract month, therefore funds rate to coincide with the average target, i.e.

(_{t i}^ef _{t i}^T ) 0

E i

₊ −

i

₊ = (6)

where

i

_{t i}^T₊ is the target rate for month t+ . Therefore, in the months with FOMC

i

meetings, the average expected FF rate for the period represents a weighted average of the FF target rate before the FOMC meeting and the expected rate for days after the meeting. When rates are expressed in percentages, this is equivalent to:

is k days into the month,

i

_{t h}^T^ˆ₊ is the estimate of the target funds rate after the meeting, and there are m days in the month with the FOMC meeting.

The expected target FF rate after the FOMC meeting can be derived as:

ˆ ,

It is often useful to convert this forecast to an anticipated probability that the FOMC changes its target rate. Then by definition:

( ) (1 )

T T T T

i = p i + Δ i + − p i

(9)

where Δ is the expected change in the target rate and p is the anticipated probability

i

^T that the FOMC changes its target. This can solve for p, yielding

100(^Tˆ ^T)

This calculation thus extracts the probability of a target change that is implied by the futures quote.

IV. Usefulness of Futures for Predicting Fed Funds Rate

In this section, we will use daily frequency data and the forecasts made at a number different days in prior to the FOMC meeting to see the usefulness of futures for predicting directional change of FF rate by applying generalized H-M test. Because a press statement describing policy action is released immediately at the conclusion of any FOMC meeting at which an action was undertaken since February 1994, market

participants regard the day as a milestone of FOMC decisions becoming more open and transparent. In order to see whether prediction power indeed greatly improved, we separated my sample into two groups of prior 1994/2 and after 1994/2. The following are procedures we applied for the empirical part of the chapter.

Because changes in the FF target rate are limited to multiples of 25 basis points since August 1989 (Poole and Rasche, 2003), and 56 of 78 times (72 percent) changes in target rates are 25 basis points. Therefore if the market participants anticipate FOMC will change the target rate, the magnitude will usually be 25 basis points. On the other hand, since we are only interested in directional change of target FF rate and the minimum change of target FF rate is 25 basis points, no matter what the magnitude is, changes of FF target rate are a multiple of 25 basis points, the probability of eq. (10) under these circumstances will remain the same by replacing Δ with 25 basis points.

i

^T By replacing Δ with 25 basis points I can get

i

100( ˆ ) 0.25%

T T

i i

P

= − (10’)

The economists might have some “rule of thumb” that anticipate target rate will be changed if

P > 0.5

and

0 < ≤ P 0.5

implies market anticipate target rate will be unchanged. In other words, for example, if

P > 0.5

and

i

_{t h}^T^ˆ₊ >

i

_{t h}^T₊ means the market anticipates the target rate will be raised. Therefore, with consideration to the actual FOMC movement, we can group my data into a 3 by 3 contingency table of predictions on different days prior to an FOMC meeting as:

Figure 3.2 Forecast and actual change of FF target rate

Then the market timing statistics,

s which is proposed by Pesaran and

Timmermann (1992, 1994)²⁷, can be computed from the cell frequencies in this table

When actual and predicted values fall in n categories the null hypothesis of no market timing can be written as

This hypothesis state that the proportion of correct predictions is equal to the proportion we would expect under the null of independence of the distribution of realized and predicted values across the categories.

To derive the asymptotic distribution of S

, let P

′ =(

P P

₁₁, ₁₂,...,

P

₁_m;

P P

₂₁, ₂₂,...;

P

_m₁,

P

_m₁,...,

P

_mm)

which turned out to be:

Table 3.1 Market timing statistics of FF futures rates

days prior to

FOMC meeting

Pre 1994/2 After 1994/2 Full range 1d 3.35 (0.00080)*** 16.55 (0)*** 13.13 (0)***

We see that market timing statistics are significant at 99% confidence level for at least 2 months prior to FOMC meetings and 90 % confidence level for at least 3 months prior to FOMC meetings of 1989/8 to 2008/3, which means FF futures rates are of great value to market participants. However, the market timing statistics increases as days approach the FOMC meeting, indicating improvement in the prediction power as more information become accessible to market participants. Comparing the columns labeled

“pre 1994/2” and “after 1994/2”, we see that the market timing statistics are much

smaller in the “pre 1994/2” period. Besides, the market timing statistics are significant at 99% level for only 3 weeks prior to FOMC meetings in the “pre 1994/2” period, but are significant for at least 2 months prior to FOMC meetings in the “after 1994/2”

period. The results indicate that there is an important shift that occurred during the early 1990s in the ability for financial markets to better anticipate monetary policy actions.

Through most of the pre 1994/2 period, market prices have had predictive power for policy actions only about 6 week ahead. More recently, however, market quotes have became much better predictors of monetary policy moves as good as several months ahead.

However, some may question that such improvement in predicting ability may not come from a more transparent monetary policy process but from the change in the philosophy of FOMC monetary operation. Since monetary policy has become more

“gradualism” in late 1990’s, it means that interest rate increases tend to be followed by additional increases and, after a turning point, decreases by additional decreases.

Therefore, the predictive accuracy is lowest around policy cycle turning points (Carlson and McIntire, 1995). In order to see whether the predictive power also improved at policy cycle turning points, we adopt the following empirical study.

We define the policy cycle turning points as whenever a direction of target rate change is different with the previous FOMC decision, which means if the previous FOMC decision is ease and current decision is no change then the current meeting is the policy cycle turning point. In other words, if previous FOMC decision is ease and current decision is ease then the current meeting is not a policy cycle turning point.

Then we can define the following 2 by 2 contingency table as follows:

Figure 3.3 Forecast and actual change of policy cycle turning point

Forecast

Turning point Not turning point

Then the market timing statistics,

s , computed from the cell frequencies in the

_n table turned out to be:

Table 3.2 Market timing statistics of policy cycle turning points

days prior to

FOMC meeting

Pre 1994/2 After 1994/2 Full range 1d 2.4928 **(0.0127) 8.1076*** (0) 9.1858*** (0) 3m 1.1779 (0.2388) 1.3450 (0.1786) 2.2025** (0.0276) 4m -0.8011 (1) 0.4470 (0.6549) 0.2784 (0.7807)

* 90% 95% *99%

Note: z-statistic (p-value)

Going down the column of Table 2 labeled “full range”, The results reinforce my points mentioned above. Going down the column of Table 3 labeled “full range”, the results are similar to Table 3.2 that market timing statistics are significant at 99%

confidence level for at least 2 months prior to FOMC meetings and 95 % confidence

the market timing statistics also increase as dates approach the FOMC meeting.

Comparing the columns labeled “pre 1994/2” and “after 1994/2”, we again see that market timing statistics are much smaller in the “pre 1994/2” period, with the market timing statistics significant at 90% level only 1 week prior to the FOMC meeting in the

“pre 1994/2” period, but are at least 2 months prior to the FOMC meeting in the “after 1994/2” period.

V. Concluding Remarks

The Federal Funds rate plays a key role in the financial and economic environment facing individuals, businesses and economists, which make accurately forecasting the rate valuable. This chapter verified the directional forecasting ability of the FF futures rates on the FF target rate. We found that the futures as proxies of predictors were of value to the user. However, the accuracy of the FF futures rates prediction generally decreases with the increase in forecast horizon. Besides, the futures based predictors were more valuable since 1994/2, the time when FOMC decisions became more open and transparent.

Appendix 3.1. Contingency tables regarding “tighten, ease or unchanged”

Table A.3.1 Forecast and actual change regarding “tighten, ease or unchanged” (full range)

days prior to FOMC meeting

n

₂₁

n

₃₁

n

₁₂

n

₂₂

n

₃₂

n

₁₃

n

₂₃

n

₃₃

1d 35 14 4 0 83 15 0 0 30

2d 33 11 4 2 86 18 0 0 27

3d 34 12 4 1 84 18 0 1 27

4d 33 16 6 2 80 20 0 1 23

1w 32 16 6 3 78 18 0 3 25

2w 33 18 5 2 77 22 0 2 22

3w 33 18 7 2 75 22 0 4 20

4w 33 19 5 2 74 24 0 4 20

5w 32 20 4 3 75 26 0 2 19

6w 32 19 5 3 71 28 0 7 16

2m 26 31 5 9 58 34 0 8 10

3m 18 32 11 13 57 32 0 8 6

4m 14 41 15 17 46 32 0 9 2

Table A.3.2 Forecast and actual change regarding “tighten, ease or unchanged” (pre 1994/2

days prior to FOMC meeting

n

₂₁

n

₃₁

n

₁₂

n

₂₂

n

₃₂

n

₁₃

n

₂₃

n

₃₃

1d 4 8 3 0 24 13 0 0 7

2d 4 6 4 0 26 15 0 0 4

3d 4 8 4 0 23 14 0 1 5

4d 4 11 5 0 20 14 0 1 4

1w 4 9 5 0 21 12 0 2 6

2w 4 11 5 0 19 13 0 2 5

3w 4 9 6 0 19 13 0 4 4

4w 4 10 5 0 18 14 0 4 4

5w 3 8 3 1 23 16 0 1 4

6w 3 8 3 1 21 14 0 3 6

2m 1 13 4 3 15 15 0 4 4

3m 0 12 10 0 18 11 0 2 2

4m 0 16 11 0 10 11 0 5 1

Table A.3.3 Forecast and actual change regarding “tighten, ease or unchanged”

(after 1994/2)

days prior to FOMC meeting

n

₂₁

n

₃₁

n

₁₂

n

₂₂

n

₃₂

n

₁₃

n

₂₃

n

₃₃

1d 31 6 1 0 59 2 0 0 23

2d 29 5 0 2 60 3 0 0 23

3d 30 4 0 1 61 4 0 0 22

4d 29 5 1 2 60 6 0 0 19

1w 28 7 1 3 57 6 0 1 19

2w 29 7 0 2 58 9 0 0 17

3w 29 9 1 2 56 9 0 0 16

4w 29 9 0 2 56 10 0 0 16

5w 29 12 1 2 52 10 0 1 15

6w 29 11 2 2 50 14 0 4 10

2m 25 18 1 6 43 19 0 4 6

3m 18 20 1 13 39 21 0 6 4

4m 14 25 4 17 36 21 0 4 1

Appendix 3.2. Contingency tables regarding the turning point of the monetary policy cycle

Table A.3.4 Forecast and actual change of policy cycle turning point (full range)

days prior to FOMC

meeting

n

₂₁

n

₁₂

n

₂₂

1d 106 15 13 46

2d 108 13 16 43

3d 109 12 17 42

4d 103 18 19 40

1w 104 17 22 37

2w 99 22 21 38

3w 94 27 21 38

4w 94 27 22 37

5w 90 31 18 41

6w 85 36 21 38

2m 60 61 16 43

3m 49 69 15 44

4m 37 81 17 41

Table A.3.5 Forecast and actual change of policy cycle turning point (pre 1994/2)

days prior to FOMC

meeting

n

₂₁

n

₁₂

n

₂₂

1d 20 11 9 18

2d 22 9 10 17

3d 21 10 10 17

4d 19 12 11 16

1w 21 10 12 15

2w 17 14 11 16

3w 15 16 12 15

4w 13 18 11 16

5w 14 17 7 20

6w 14 17 8 19

2m 6 25 6 21

3m 9 19 5 22

4m 5 23 7 19

Table A.3.6 Forecast and actual change of policy cycle turning point (after 1994/2)

days prior to FOMC

meeting

n

₂₁

n

₁₂

n

₂₂

1d 86 4 4 28

2d 86 4 6 26

3d 88 2 7 25

4d 84 6 8 24

1w 83 7 10 22

2w 82 8 10 22

3w 79 11 9 23

4w 81 9 11 21

5w 76 14 11 21

6w 71 19 13 19

2m 54 36 10 22

3m 40 50 10 22

4m 32 58 10 22

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