Every equation on this site uses the symbols below. A symbol keeps one meaning across the anchored and Bayesian families, so a reader who learns it on one page can read it on the next. Where a symbol has a setting or an output, the name is given beside it. Hyphenated names belong to the separate panel workflow; posterior outputs lists the main API’s underscore names.
Indices
| \(t\) |
The target period being estimated |
| \(i\) |
A past period in the history the method learns from |
| \(j\) |
A reading of growth: \(0\) for the prior, \(M\) for model, \(C\) consensus |
| \(n\) |
The number of observations in a history sample; \(n_j\) for reading \(j\) |
Levels
Lowercase letters are levels, in the units the KPI is reported in.
| \(y_t\) |
The reported actual |
|
| \(y_{t-1}\) |
The latest actual reported before \(t\), the growth base |
|
| \(m_t\) |
The model’s forecast |
model |
| \(c_t\) |
The consensus |
consensus |
| \(c_{-30}\) |
The consensus read 30 days earlier |
|
| \(c_t^*\) |
The consensus after bias correction |
adjusted-consensus |
| \(d_t\) |
The analyst dispersion around consensus |
consensus-stdev |
| \(k_t\) |
The number of contributing analysts |
consensus-count |
| \(\hat y_t\) |
The published level |
prediction |
Anchored family
The anchored family works in surprise space, relative to consensus.
| \(\Delta\) |
The gap, \((m-c)/\lvert c\rvert\) |
consensus_gap |
| \(r\) |
The revision, \(c/c_{-30}-1\) |
|
| \(s\) |
The surprise, \(y/c-1\), known only after the report |
|
| \(\hat s\) |
The expected surprise |
expected_surprise |
| \(a\) |
The customary beat, the intercept |
customary_beat |
| \(b_\Delta\) |
The gap weight |
gap_weight |
| \(b_r\) |
The revision weight |
revision_weight |
Bayesian family: growth and the blend
The Bayesian family works in growth space: a level \(v\) becomes the growth \(v/y_{t-1}-1\).
| \(\theta_t\) |
The unknown growth being estimated |
|
| \(g_t\) |
Realised growth, \(y_t/y_{t-1}-1\) |
actual-growth |
| \(x_{M,t}\) |
Model growth, \(m_t/y_{t-1}-1\) |
model-growth |
| \(x_{C,t}\) |
Consensus growth, \(c_t^*/y_{t-1}-1\) |
consensus-growth |
| \(x_C^{\mathrm{raw}}\) |
Consensus growth before bias correction, \(c_t/y_{t-1}-1\) |
|
| \(\mu_0\) |
The prior mean, the mean of realised growth |
prior-mean |
| \(e_{j,i}\) |
The error of reading \(j\) against realised growth \(g_i\) |
|
| \(\sigma_j^2\) |
The variance of reading \(j\) |
|
| \(\tau_j\) |
The precision of reading \(j\), \(1/\sigma_j^2\) |
|
| \(\tau_0\) |
The prior precision |
prior-precision |
| \(\tau_M\) |
The model precision |
model-precision |
| \(\tau_C\) |
The consensus precision |
consensus-precision |
| \(T\) |
The total precision, \(\tau_0+\tau_M+\tau_C\) |
total-precision |
| \(w_j\) |
The weight of reading \(j\), \(\tau_j/T\) |
|
| \(w_0\) |
The prior weight |
prior-weight |
| \(w_M\) |
The model weight |
model-weight |
| \(w_C\) |
The consensus weight |
consensus-weight |
| \(\hat\theta\) |
The posterior growth |
posterior-growth |
| \(\sigma_\theta\) |
The posterior standard deviation, \(T^{-1/2}\) |
posterior-growth-stdev |
| \(\varepsilon\) |
The numerical floor, \(10^{-12}\) |
|
Bayesian family: options
| \(\lambda\) |
The share of the consensus bias removed |
consensus_bias_lambda |
| \(\rho_i\) |
The relative consensus error, \((c_i-y_i)/y_i\) |
|
| \(\beta_t\) |
The filtered consensus bias; published as \(100\beta_t\) |
consensus-bias-pct |
| \(K_i\) |
The Kalman gain |
|
| \(P_i\) |
The variance of the bias estimate |
|
| \(Q\) |
The process variance of the bias |
consensus_bias_process_noise |
| \(R\) |
The measurement variance of each error |
consensus_bias_measurement_noise |
| \(\delta_t\) |
Dispersion as growth, \(d_t/\lvert y_{t-1}\rvert\) |
consensus-stdev-growth |
| \(\kappa\) |
The dispersion variance multiplier |
consensus_stdev_variance_multiplier |
| \(\alpha\) |
The analyst count exponent |
consensus_count_exponent |
Bayesian family: intervals and direction
| \(p\) |
The interval coverage |
interval_width |
| \(\nu\) |
The Student-t degrees of freedom |
interval_df |
| \(\ell\) |
The Student-t location |
interval_loc |
| \(\omega\) |
The Student-t scale |
interval_scale |
| \(z_i\) |
The standardised residual, \((g_i-\hat\theta_i)/\sigma_{\theta,i}\) |
standardised-residual |
| \(F\) |
The distribution of \(z\): Student-t or empirical |
interval_method |
| \(q_L\) |
The lower quantile of \(F\), at \((1-p)/2\) |
|
| \(q_U\) |
The upper quantile of \(F\), at \(1-(1-p)/2\) |
|
| \(\theta_L\) |
The lower growth bound |
posterior-growth-lower |
| \(\theta_U\) |
The upper growth bound |
posterior-growth-upper |
| \(\gamma\) |
The standardised consensus gap, \((x_C^{\mathrm{raw}}-\hat\theta)/\sigma_\theta\) |
standardised-consensus-gap |
Correlation-adjusted method
| \(u_i\) |
The joint growth vector \((g_i, x_{C,i}, x_{M,i})^\top\) |
| \(\mu\) |
The joint mean, split into \(\mu_g\) for realised growth and \(\mu_S\) for the signals |
| \(\Sigma\) |
The joint covariance, split into blocks for \(g\) and the signals \(S=(C,M)\) |