# Amazon.com, Inc. (AMZN)

Amazon.com, Inc. is an American multinational technology company focusing on e-commerce, cloud computing, online advertising, digital streaming, and artificial intelligence.

## Stock Price Trends

Stock price trends estimated using linear regression.

#### Key facts

- The primary trend is increasing.
- The growth rate of the primary trend is 88.27% per annum.
- AMZN price at the close of December 8, 2023 was $147.42 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 11.20% per annum.
- AMZN price at the close of December 8, 2023 was higher than the top border of the secondary price channel by $0.42 (0.28%).

### Linear Regression Model

Model equation:

Y_{i} = α + β × X_{i} + ε_{i}

Top border of price channel:

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

Bottom border of price channel:

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

where:

i - observation number

Y_{i} - natural logarithm of AMZN 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: November 18, 2022

End date: September 20, 2023

a = 1.9349

b = 0.0017

s = 0.0528

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0017) – 1

= 88.27%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0528) – 1

= 23.51%

#### November 18, 2022 calculations

Top border of price channel:

Exp(Y_{994})

= Exp(a + b × X_{994} + 2 × s)

= Exp(a + b × 1,439 + 2 × s)

= Exp(1.9349 + 0.0017 × 1,439 + 2 × 0.0528)

= Exp(4.5348)

= $93.21

Bottom border of price channel:

Exp(Y_{994})

= Exp(a + b × X_{994} – 2 × s)

= Exp(a + b × 1,439 – 2 × s)

= Exp(1.9349 + 0.0017 × 1,439 – 2 × 0.0528)

= Exp(4.3237)

= $75.46

#### September 20, 2023 calculations

Top border of price channel:

Exp(Y_{1,202})

= Exp(a + b × X_{1,202} + 2 × s)

= Exp(a + b × 1,745 + 2 × s)

= Exp(1.9349 + 0.0017 × 1,745 + 2 × 0.0528)

= Exp(5.0653)

= $158.42

Bottom border of price channel:

Exp(Y_{1,202})

= Exp(a + b × X_{1,202} – 2 × s)

= Exp(a + b × 1,745 – 2 × s)

= Exp(1.9349 + 0.0017 × 1,745 – 2 × 0.0528)

= Exp(4.8541)

= $128.26

### Secondary Trend

Start date: May 26, 2023

End date: November 6, 2023

a = 4.3786

b = 0.0003

s = 0.0407

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0003) – 1

= 11.20%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0407) – 1

= 17.67%

#### May 26, 2023 calculations

Top border of price channel:

Exp(Y_{1,123})

= Exp(a + b × X_{1,123} + 2 × s)

= Exp(a + b × 1,628 + 2 × s)

= Exp(4.3786 + 0.0003 × 1,628 + 2 × 0.0407)

= Exp(4.9334)

= $138.86

Bottom border of price channel:

Exp(Y_{1,123})

= Exp(a + b × X_{1,123} – 2 × s)

= Exp(a + b × 1,628 – 2 × s)

= Exp(4.3786 + 0.0003 × 1,628 – 2 × 0.0407)

= Exp(4.7707)

= $118.01

#### November 6, 2023 calculations

Top border of price channel:

Exp(Y_{1,235})

= Exp(a + b × X_{1,235} + 2 × s)

= Exp(a + b × 1,792 + 2 × s)

= Exp(4.3786 + 0.0003 × 1,792 + 2 × 0.0407)

= Exp(4.9811)

= $145.64

Bottom border of price channel:

Exp(Y_{1,235})

= Exp(a + b × X_{1,235} – 2 × s)

= Exp(a + b × 1,792 – 2 × s)

= Exp(4.3786 + 0.0003 × 1,792 – 2 × 0.0407)

= Exp(4.8184)

= $123.77