# Amazon.com Inc (AMZN)

Amazon.com, Inc. is an American multinational technology company which focuses on e-commerce, cloud computing, digital streaming, and artificial intelligence. It is one of the Big Five companies in the U.S. information technology industry, along with Google, Apple, Microsoft, and Facebook. The company has been referred to as one of the most influential economic and cultural forces in the world, as well as the world's most valuable brand.

## 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 69.68% per annum.
- AMZN price at the close of April 16, 2024 was $183.32 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 106.49% per annum.
- AMZN price at the close of April 16, 2024 was inside the secondary price channel.

### 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: April 16, 2024

a = 2.5604

b = 0.0014

s = 0.0549

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0014) – 1

= 69.68%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0549) – 1

= 24.55%

#### November 18, 2022 calculations

Top border of price channel:

Exp(Y_{906})

= Exp(a + b × X_{906} + 2 × s)

= Exp(a + b × 1,311 + 2 × s)

= Exp(2.5604 + 0.0014 × 1,311 + 2 × 0.0549)

= Exp(4.5693)

= $96.47

Bottom border of price channel:

Exp(Y_{906})

= Exp(a + b × X_{906} – 2 × s)

= Exp(a + b × 1,311 – 2 × s)

= Exp(2.5604 + 0.0014 × 1,311 – 2 × 0.0549)

= Exp(4.3497)

= $77.45

#### April 16, 2024 calculations

Top border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} + 2 × s)

= Exp(a + b × 1,826 + 2 × s)

= Exp(2.5604 + 0.0014 × 1,826 + 2 × 0.0549)

= Exp(5.3153)

= $203.42

Bottom border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} – 2 × s)

= Exp(a + b × 1,826 – 2 × s)

= Exp(2.5604 + 0.0014 × 1,826 – 2 × 0.0549)

= Exp(5.0957)

= $163.32

#### Description

- The primary trend is increasing.
- The growth rate of the primary trend is 69.68% per annum.
- AMZN price at the close of April 16, 2024 was $183.32 and was inside the primary price channel.

### Secondary Trend

Start date: September 26, 2023

End date: April 16, 2024

a = 1.6136

b = 0.0020

s = 0.0273

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0020) – 1

= 106.49%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0273) – 1

= 11.54%

#### September 26, 2023 calculations

Top border of price channel:

Exp(Y_{1,118})

= Exp(a + b × X_{1,118} + 2 × s)

= Exp(a + b × 1,623 + 2 × s)

= Exp(1.6136 + 0.0020 × 1,623 + 2 × 0.0273)

= Exp(4.8923)

= $133.25

Bottom border of price channel:

Exp(Y_{1,118})

= Exp(a + b × X_{1,118} – 2 × s)

= Exp(a + b × 1,623 – 2 × s)

= Exp(1.6136 + 0.0020 × 1,623 – 2 × 0.0273)

= Exp(4.7830)

= $119.47

#### April 16, 2024 calculations

Top border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} + 2 × s)

= Exp(a + b × 1,826 + 2 × s)

= Exp(1.6136 + 0.0020 × 1,826 + 2 × 0.0273)

= Exp(5.2955)

= $199.44

Bottom border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} – 2 × s)

= Exp(a + b × 1,826 – 2 × s)

= Exp(1.6136 + 0.0020 × 1,826 – 2 × 0.0273)

= Exp(5.1863)

= $178.80

#### Description

- The secondary trend is increasing.
- The growth rate of the secondary trend is 106.49% per annum.
- AMZN price at the close of April 16, 2024 was inside the secondary price channel.