Gold Price Prediction Models

Predictive models for gold prices typically use classical time-series and econometric techniques. Below we outline the main approaches with their key equations and examples of typical specifications.

Time-Series Models

• ARIMA (Autoregressive Integrated Moving Average): This univariate model fits gold’s own history. In general, an ARIMA(p,d,q) model is written as ΔdPt=α+∑i=1pϕi ΔdPt−i+∑j=1qθj εt−j+εt,\Delta^d P_t = \alpha + \sum_{i=1}^p \phi_i\,\Delta^d P_{t-i} + \sum_{j=1}^q \theta_j\,\varepsilon_{t-j} + \varepsilon_t, where $P_t$ is (e.g.) the gold price, $\Delta^d$ denotes differencing of order $d$, and $\varepsilon_t$ is white noise (untitled). For example, many studies find that simple forms like ARIMA(1,1,1) or (0,1,1) can capture gold’s trends in the short term (.) (.). (Here ARIMA(1,1,1) means $P_t – P_{t-1} = \alpha + \phi_1(P_{t-1}-P_{t-2}) + \theta_1\varepsilon_{t-1} + \varepsilon_t$.) Seasonal ARIMA (SARIMA) models can be used if gold shows calendar effects. In practice one fits ARIMA by ensuring stationarity (e.g. via Augmented Dickey–Fuller tests) and choosing $p,q$ by autocorrelation/PACF analysis (untitled).
• Autoregressive (AR) and Moving-Average (MA) models: An AR(p) model uses only past gold values: Pt=α+∑i=1pϕiPt−i+εt,P_t = \alpha + \sum_{i=1}^p \phi_i P_{t-i} + \varepsilon_t, while an MA(q) model uses past shocks: Pt=μ+εt+∑j=1qθj εt−j.P_t = \mu + \varepsilon_t + \sum_{j=1}^q \theta_j\,\varepsilon_{t-j}. An ARMA(p,q) combines both. These are special cases of ARIMA with $d=0$. For example, one forecasting study used an AR(5) (multiple regression on 5 lags of price) as its model (.).
• Vector Autoregression (VAR): A VAR treats gold jointly with other time series (e.g. USD index, interest rates, oil). In matrix form for a $k$-variate system: rt=Φ0+Φ1rt−1+⋯+Φprt−p+at,r_t = \Phi_0 + \Phi_1 r_{t-1} + \cdots + \Phi_p r_{t-p} + a_t, where $r_t$ is a $k\times1$ vector of variables (for example $(\text{gold price}_t,\text{USD}_t,\text{yield}_t,\dots)^T$) (untitled). For instance, a VAR(1) might model gold and the US dollar index together as (PtDt)=Φ0+Φ1(Pt−1Dt−1)+(εPtεDt).\begin{pmatrix} P_t \\ D_t\end{pmatrix} = \Phi_0 + \Phi_1 \begin{pmatrix} P_{t-1} \\ D_{t-1}\end{pmatrix} + \begin{pmatrix}\varepsilon_{Pt}\\ \varepsilon_{Dt}\end{pmatrix}.
  (VAR models are often estimated by ordinary least squares on each equation; see Eq. (3) in (untitled).) A VAR can capture feedback among gold, currencies and rates. Relatedly, ARIMAX or transfer-function models simply add exogenous predictors (like inflation) to an ARIMA specification. In practice, mixed models like ARIMA with exogenous variables or VARs have been used to include macro factors (inflation, yields, USD index) in gold forecasting.
• Example (ARIMA): One study using Box–Jenkins found that an ARIMA(1,1,1) model gave a reasonable short-term fit to gold price returns, although forecasting errors can be large (untitled). Another analysis of Thai gold prices selected ARIMA(1,1,1) by AIC (.). (In contrast, Massarrat (2013) found ARIMA(0,1,1) was best in his sample (.).)
• Example (VAR): Researchers have also applied VAR to gold and related series. For example, a VAR system might include (log) gold price, (log) dollar index and (log) oil price, and estimate =\Phi_0 + \Phi_1\begin{pmatrix}\ln P_{t-1}\\\ln D_{t-1}\\\ln O_{t-1}\end{pmatrix} + \cdots.$$ Such multivariate time-series models capture the joint dynamics and are often estimated via lagged OLS regression ([untitled](https://www.cse.wustl.edu/~yixin.chen/public/GoldPrice.pdf#:~:text=determined%20by%20its%20trend%2C%20but,where%20%DD%8E%E0%AF%A7%20%E0%B5%8C%20%E0%B5%AB%DD%8E%E0%AC%B5%2C%E0%AF%A7%2C%E2%80%A6%2C%DD%8E%E0%AF%9E%2C%E0%AF%A7%E0%B5%AF%20%E0%AF%8D)).

Regression and Cointegration Models

• Multiple Linear Regression (OLS): Another common approach is to regress the gold price (or log price) on economic variables like inflation, interest rates and currency indexes. A general form is Pt=α+∑iβiXi,t+εt.P_t = \alpha + \sum_i \beta_i X_{i,t} + \varepsilon_t. For example, one study regressed log (gold price) on log (US dollar index), log (CPI), log (major stock index) and the Fed funds rate. Their estimated model was: ln⁡P=−19.1287  −  0.5320 ln⁡(USD)  +  6.5508 ln⁡(CPI)  −  0.7311 ln⁡(DJIA)  −  0.01346 RATE,\ln P = -19.1287 \;-\;0.5320\,\ln(\text{USD}) \;+\;6.5508\,\ln(\text{CPI}) \;-\;0.7311\,\ln(\text{DJIA}) \;-\;0.01346\,RATE, (with $R^2\approx0.975$). This implies that, as expected, gold rises strongly with inflation ($\beta\approx6.55$ on $\ln(\text{CPI})$) and falls when the dollar or stock market rise. More generally, many regressions confirm positive links to inflation/money supply and negative links to interest rates or USD (untitled). For instance, one analysis notes “gold price is positively linked with CPI, M2 and negatively linked with interest rates” (untitled).
• Currency Effects: The gold–USD relationship is often modeled by including a dollar index or exchange rate as a regressor. A strong USD normally pushes gold down. The World Gold Council’s regression model (GRAM) finds that recent gold declines were driven primarily by a rise in the US dollar index (Gold Market Commentary: January jitters | World Gold Council). In OLS terms, this corresponds to a negative coefficient on the dollar index as seen above.
• Currency & Macro Examples: Other models use variables like real interest rates or bond yields. For example, PIMCO regressed the real (inflation-adjusted) gold price on the 10-year U.S. TIPS yield and found that a 100 bp increase in real yield corresponds to about a 24% drop in real gold price (Understanding Gold Prices | PIMCO) (implying “gold has a real duration of 24 years”). In formulaic terms, one can write ln⁡(Pt/CPIt)=α+β (y10yr,treal)+εt,\ln(P_t/CPI_t) = \alpha + \beta\,(y^{\text{real}}_{10yr,t}) + \varepsilon_t, with estimated $\beta<0$ (Understanding Gold Prices | PIMCO). This captures the notion that higher real interest rates (rising yield) lower gold’s appeal.
• Econometric Cointegration / VECM: If gold price and a macro variable are nonstationary but move together, a cointegrating (long-run equilibrium) relation can be imposed. For example, one study estimated a cointegrating equation among Pakistani gold price ($GP$), GDP, interest ($INT$), USD/PKR forex and commodity prices. Their long-run equilibrium was: GPt−1=14007.4+31.243 GPDt−1+842.43 INTt−1+500.49 FOREXt−1−8410.99 ln⁡(SPt−1)−817.74 ln⁡(SMPt−1),GP_{t-1} = 14007.4 + 31.243\,GPD_{t-1} + 842.43\,INT_{t-1} + 500.49\,FOREX_{t-1} – 8410.99\,\ln(SP_{t-1}) – 817.74\,\ln(SMP_{t-1}), (where $GPD$=global gold price, $SP$=silver price, $SMP$=stock market cap). In short-run form, an Error-Correction Model (ECM) was fit. One estimated VECM took the form ΔGPt=0.5143 ECTt−1+0.6679 ΔGPt−1+1.4923 ΔGPDt−1+40.1903 ΔINTt−1−241.2813 ΔFOREXt−1+⋯+397.87, \Delta GP_t = 0.5143\,ECT_{t-1} + 0.6679\,\Delta GP_{t-1} + 1.4923\,\Delta GPD_{t-1} + 40.1903\,\Delta INT_{t-1} – 241.2813\,\Delta FOREX_{t-1} + \dots + 397.87, where $ECT_{t-1}$ is the one-period lagged cointegration error. Such ECM models blend short-term dynamics with the long-run equilibrium constraint.
• Inflation/Money-Supply Models: Many models are inspired by the idea that gold is an inflation or monetary hedge. Empirically, gold tends to move with broad money or inflation. One study explicitly found cointegration between gold and the U.S. money supply (M2), though not with CPI alone (Beyond CPI: Gold as a strategic inflation hedge). In practice, regressions often include terms like $\ln(M2_t)$ or a CPI measure. For example, some specifications use the quantity-theory approach $P_t \sim \alpha + \beta,\ln(M2_t) + \gamma,\ln(\text{CPI}_t) + \dots$. As cited above, an estimated coefficient of $\sim6.55$ on $\ln(\text{CPI})$ indicates gold’s sensitivity to inflation. Correspondingly, studies often report negative coefficients on real interest rates (capturing opportunity cost) and USD strength (untitled).

Key Equations Recap: Summarizing, typical forecasting formulas include

• ARIMA: $\Delta^d P_t = \alpha + \sum_{i=1}^p\phi_i,\Delta^dP_{t-i} + \sum_{j=1}^q\theta_j,\varepsilon_{t-j} + \varepsilon_t$ (untitled).
• VAR: $r_t = \Phi_0 + \Phi_1 r_{t-1} + \dots + \Phi_p r_{t-p} + a_t$ (untitled).
• OLS Regression: $P_t = \alpha + \beta_1 X_{1,t} + \beta_2 X_{2,t} + \cdots + \varepsilon_t$, e.g. $\ln P = -19.13 -0.532\ln(\text{USD}) +6.551\ln(\text{CPI}) -0.731\ln(\text{DJIA}) -0.0135,RATE$.
• ECM/VECM: $0 = P_t – (a + b X_t + \dots)$ (long-run cointegration), and $\Delta P_t = \alpha,ECT_{t-1} + \sum \gamma_i,\Delta X_{t-i} + \varepsilon_t$.

In practice, models often combine these ideas (e.g. ARIMAX with macro inputs, or a VAR with cointegration). The literature consistently finds that inflation/real money variables and real interest rates (or USD strength) are among the dominant predictors (untitled) (Understanding Gold Prices | PIMCO), so these enter the formulas above either directly or via lagged relations (as in a VECM). All models rest on standard assumptions (stationarity after differencing, linearity, exogeneity of regressors, etc.) and their fit is evaluated by forecasting metrics (RMSE, AIC, etc.) as seen in the cited studies.

Sources: Academic and industry studies provide the above models and equations (untitled) (.) (untitled) (Understanding Gold Prices | PIMCO), as do practitioner frameworks (e.g. World Gold Council’s regression models (Gold Market Commentary: January jitters | World Gold Council)). These references illustrate the forms of the formulas and their empirical coefficients.