May 222015
 

I keep in touch with the work of academics interested in gold via this website and it is a humbling experience. It reminds me of the saying “those who can’t do, teach; those who can’t teach, blog” (I thought it needed updating).

That website recently posted a September 2014 paper by Dirk Baur, Joscha Beckmann & Robert Czudaj called Gold Price Forecasts in a Dynamic Model Averaging Framework – Have the Determinants Changed Over Time?

No doubt you have seen many commentators writing about their forecasts for the gold price and giving reasons (which is basically their “model” for what drives the gold price). But I bet you have never seen a gold forecasting blog post that include one of these:

formula

That comes from Dirk et al.’s (lets call them Dirk’s team) paper and no, I don’t know what it means, it has something to do with knowing “the conditional distribution of the state at time t−1 given the time t−1 information set Y t−1 = y1, . . . , yt−1”. What I do know is that this hard core approach means what the academics do is rigorous.

I’ve met Dirk a few times when he was at the University of Technology in Sydney, he is now at Kühne Logistics University. Last time I met him he described how he had to present a paper in front of a bunch of other academics, where they do their best to rip it to shreds and/or ask lots of difficult questions. This is standard stuff for academics and it means people avoid circulating rubbish. I don’t think many bloggers would be willing to go through a similar approach.

Anyway, the reason I’ve highlighted Dirk’s team paper is because it proves that the things that drive the gold price change over time and more usefully, what the key ones are and their changing influence on gold. Most of the more serious forecasters usually create a fixed formula based on some variables, see this one by Eddy Elfenbein for an example – which simplifies to:

(((this month’s 2% Deflator/this month’s Ibbotson Real Rate/(last month’s 2% Deflator/last month’s Ibbotson Real Rate)-1)*8+1)*last month’s gold price)

Other models have a lot more variables, such as “commodity prices, interest rates, inflation expectations, exchange rate changes and stock market volatility among others”. What Dirk’s team show is that in addition to working out what weights each of these variables need to have in your formula, you also have to work out how those weightings change over time. This makes sense, because the world isn’t flat and things change. For example, Dirk’s team note that the influence of the stock market on gold is generally higher during times of turbulence.

As you can imagine, trying to work out which variables matter, what weightings they should have and how those weightings should change over time is a pretty tricky exercise and results in a “computational burden” due to “the need of determining a transition matrix Bayesian inference” (I don’t know what that means, which is why I used the word “tricky”). Dirk’s team calculate that a forecasting model with 14 variables results in 16,384 formulas to test, and that is without changing the weightings!

So Dirk’s team used a Dynamic Model Averaging approach which involves some sequential learning in the forecasting procedure. The interesting take aways for me from the paper include:

  • generally only two or three variables are driving gold prices at any one time
  • there are brief periods where you need six or seven variables to model the gold price
  • US CPI played a big role during the 1970s but is insignificant during the “great moderation” between 1980 and mid-2000
  • gold is influenced more by world CPI levels than by US CPI levels
  • silver prices had a strong influence on gold between 1995 and 2005
  • there are significant changes in the mix of variables around the Millennium
  • weak evidence for the importance of stock markets, even during financial crises

At the end of the paper Dirk’s team include charts of the key variables they looked at, which show how useful a variable is in forecasting the gold price (the closer to 1 the more important the variable). Below are four I picked out.

variable

These charts clearly demonstrate the complexity of the gold market – the factors that influence it are dynamic, changing over time. It is like gold is a melting pot of the diverse views of market participants, which probably accounts for why it has a low to zero correlation to most asset classes.

The problem with all models of the gold price is that you have to forecast what the underlying variables will be to get a forecast for the gold price. Dirk, Joscha & Robert’s work shows that you now have to also forecast the importance of each variable, making the task doubly complicated. Something to keep in mind the next time you see a talking head on TV say that gold is going to go up or down because of their view about one single variable they think explains all.