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## Stock Price Trends

Stock price trends estimated using linear regression.

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#### Key facts

- The primary trend is increasing.
- The growth rate of the primary trend is 11.18% per annum.
- AAPL price at the close of June 8, 2023 was $180.57 and was inside the primary trend channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 101.88% per annum.
- AAPL price at the close of June 8, 2023 was inside the secondary trend channel.

### Linear Regression Model

Model equation:

Y_{i} = α + β × X_{i} + ε_{i}

Top border of trend channel:

Exp(Y_{i}) = Exp(a + b × X_{i} + 2 × s)

Bottom border of trend channel:

Exp(Y_{i}) = Exp(a + b × X_{i} – 2 × s)

where:

i - observation number

Y_{i} - natural logarithm of AAPL price

X_{i} - time index, 1 day interval

σ - standard deviation of ε_{i}

a - estimator of α

b - estimator of β

s - estimator of σ

Exp() - calculates the exponent of e

### Primary Trend

Start date:

End date:

a =

b =

s =

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × ) – 1

=

Trend channel spread:

Exp(4 × s) – 1

= Exp(4 × ) – 1

=

#### August 5, 2020 calculations

Top border of trend channeld:

Exp(Y_{})

= Exp(a + b × X_{} + 2 × s)

= Exp(a + b × + 2 × s)

= Exp( + × + 2 × )

= Exp()

= $

Bottom border of trend channel:

Exp(Y_{})

= Exp(a + b × X_{} – 2 × s)

= Exp(a + b × – 2 × s)

= Exp( + × – 2 × )

= Exp()

= $

#### June 8, 2023 calculations

Top border of trend channel:

Exp(Y_{})

= Exp(a + b × X_{} + 2 × s)

= Exp(a + b × + 2 × s)

= Exp( + × + 2 × )

= Exp()

= $

Bottom border of trend channel:

Exp(Y_{})

= Exp(a + b × X_{} – 2 × s)

= Exp(a + b × – 2 × s)

= Exp( + × – 2 × )

= Exp()

= $

### Secondary Trend

Start date:

End date:

a =

b =

s =

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × ) – 1

=

Trend channel spread:

Exp(4 × s) – 1

= Exp(4 × ) – 1

=

#### December 16, 2022 calculations

Top border of trend channel:

Exp(Y_{})

= Exp(a + b × X_{} + 2 × s)

= Exp(a + b × + 2 × s)

= Exp( + × + 2 × )

= Exp()

= $

Bottom border of trend channel:

Exp(Y_{})

= Exp(a + b × X_{} – 2 × s)

= Exp(a + b × – 2 × s)

= Exp( + × – 2 × )

= Exp()

= $

#### June 8, 2023 calculations

Top border of trend channel:

Exp(Y_{})

= Exp(a + b × X_{} + 2 × s)

= Exp(a + b × + 2 × s)

= Exp( + × + 2 × )

= Exp()

= $

Bottom border of trend channel:

Exp(Y_{})

= Exp(a + b × X_{} – 2 × s)

= Exp(a + b × – 2 × s)

= Exp( + × – 2 × )

= Exp()

= $