# Apple Inc. (NASDAQ:AAPL) Discover a new approach to trend analysis.
Check the power of mathematical statistics.
Trend channels has never been so accurate.

## Stock Price Trends

Stock price trends estimated using linear regression.

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We accept:            #### 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:
Yi = α + β × Xi + εi

Top border of trend channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)

Bottom border of trend channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)

where:

i - observation number
Yi - natural logarithm of AAPL price
Xi - time index, 1 day interval
σ - standard deviation of εi
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
=

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
=

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()
= \$