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  2. Autoregressive moving-average model - Wikipedia

    en.wikipedia.org/wiki/Autoregressive_moving...

    MATLAB includes functions such as arma, ar and arx to estimate autoregressive, exogenous autoregressive and ARMAX models. See System Identification Toolbox and Econometrics Toolbox for details. Julia has community-driven packages that implement fitting with an ARMA model such as arma.jl.

  3. Multiplicative group of integers modulo n - Wikipedia

    en.wikipedia.org/wiki/Multiplicative_group_of...

    Indeed, a is coprime to n if and only if gcd(a, n) = 1. Integers in the same congruence class a ≡ b (mod n) satisfy gcd(a, n) = gcd(b, n); hence one is coprime to n if and only if the other is. Thus the notion of congruence classes modulo n that are coprime to n is well-defined.

  4. Modulo - Wikipedia

    en.wikipedia.org/wiki/Modulo

    In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.

  5. Autoregressive integrated moving average - Wikipedia

    en.wikipedia.org/wiki/Autoregressive_integrated...

    Specifically, ARMA assumes that the series is stationary, that is, its expected value is constant in time. If instead the series has a trend (but a constant variance/autocovariance), the trend is removed by "differencing", [1] leaving a stationary series. This operation generalizes ARMA and corresponds to the "integrated" part of ARIMA ...

  6. Multiplicative order - Wikipedia

    en.wikipedia.org/wiki/Multiplicative_order

    This is the group of units of the ring Z n; it has φ(n) elements, φ being Euler's totient function, and is denoted as U(n) or U(Z n). As a consequence of Lagrange's theorem, the order of a (mod n) always divides φ(n). If the order of a is actually equal to φ(n), and therefore as large as possible, then a is called a primitive root modulo n.

  7. Primitive root modulo n - Wikipedia

    en.wikipedia.org/wiki/Primitive_root_modulo_n

    And then, Euler's theorem says that a φ (n) ≡ 1 (mod n) for every a coprime to n; the lowest power of a that is congruent to 1 modulo n is called the multiplicative order of a modulo n. In particular, for a to be a primitive root modulo n , a φ ( n ) has to be the smallest power of a that is congruent to 1 modulo n .

  8. Help:Convert units - Wikipedia

    en.wikipedia.org/wiki/Help:Convert_units

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  9. Modular multiplicative inverse - Wikipedia

    en.wikipedia.org/wiki/Modular_multiplicative_inverse

    As the product of two units is a unit, the units of a ring form a group, the group of units of the ring and often denoted by R × if R is the name of the ring. The group of units of the ring of integers modulo m is called the multiplicative group of integers modulo m, and it is isomorphic to a reduced residue system.