Forecasting
Introduction
The first part of the forecasting involves a matrix multiplication, where we multiply the factors by the factors combination.
Case study: the Amar model
For the Amar model, the resulting median rolling out of sample information coefficient across coins is 16%. This is above the initial target of 10%; we therefore consider these results to be robust and exceeding expectations.
In particular, we notice stronger out of sample performance for alt-coins.
It is also reassuring to see strong correlations in the out of sample set, from July 2022 up to June 2023 as one can notice in figures 1 and 2 for ETH as an example, despite this period being one of the most difficult in crypto with many exogenous shocks resulting from central banks policies, news and sentiment.
Converting forecasts to probabilities of downside moves
Now that we have generated robust forecasts, we must convert them into probabilities of downside moves and estimate the CDF (Cumulative Distribution Function).
The goal is to estimate empirically the probability of a move of less than q in the n days horizon, where q is in percent returns (10% for example).
We apply the following approach:
i. Derive the error, defined as: error=y_hat-y_actual
ii. Iteratively and for each forecast (with a minimum sample size of 1,000): derive the standard error, defined as: SE=(std(error))/(sqrt(n-2)), where n is the sub sample size
iii. At the 99.9% confidence level, the t-stat is 3.291, hence the upper/lower bands for the prediction interval are defined as:
upper⁄lower=forecast+-t_99.9*S.E.
iv. Apply a margin of error on the prediction interval estimation, hence:
upper⁄lower= upper⁄lower+ abs( upper⁄lower) × margin_error
v. The probabilities given q can be estimated using alinear interpolation following the formula:
min(max((q-lower)/(upper-lower),0),1)
vi. Apply a smoothing factor with is an exponentially weighted moving average
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