## Stock Price Trends

Stock price trends estimated using linear regression.

### Summary

#### Key facts

- The primary trend is decreasing.
- The decline rate of the primary trend is 77.74% per annum.
- SMCI price at the close of November 11, 2024 was $23.23 and was lower than the bottom border of the primary price channel by $7.63 (24.71%).
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 93.10% per annum.
- SMCI price at the close of November 11, 2024 was lower than the bottom border of the secondary price channel by $0.03 (0.14%).

### 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 SMCI 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: March 4, 2024

End date: October 30, 2024

a = 11.2170

b = -0.0041

s = 0.1359

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × -0.0041) – 1

= -77.74%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.1359) – 1

= 72.21%

#### March 4, 2024 calculations

Top border of price channel:

Exp(Y_{1,082})

= Exp(a + b × X_{1,082} + 2 × s)

= Exp(a + b × 1,574 + 2 × s)

= Exp(11.2170 + -0.0041 × 1,574 + 2 × 0.1359)

= Exp(5.0101)

= $149.92

Bottom border of price channel:

Exp(Y_{1,082})

= Exp(a + b × X_{1,082} – 2 × s)

= Exp(a + b × 1,574 – 2 × s)

= Exp(11.2170 + -0.0041 × 1,574 – 2 × 0.1359)

= Exp(4.4666)

= $87.06

#### October 30, 2024 calculations

Top border of price channel:

Exp(Y_{1,249})

= Exp(a + b × X_{1,249} + 2 × s)

= Exp(a + b × 1,814 + 2 × s)

= Exp(11.2170 + -0.0041 × 1,814 + 2 × 0.1359)

= Exp(4.0222)

= $55.83

Bottom border of price channel:

Exp(Y_{1,249})

= Exp(a + b × X_{1,249} – 2 × s)

= Exp(a + b × 1,814 – 2 × s)

= Exp(11.2170 + -0.0041 × 1,814 – 2 × 0.1359)

= Exp(3.4787)

= $32.42

#### Description

- The primary trend is decreasing.
- The decline rate of the primary trend is 77.74% per annum.
- SMCI price at the close of November 11, 2024 was $23.23 and was lower than the bottom border of the primary price channel by $7.63 (24.71%).

### Secondary Trend

Start date: June 13, 2024

End date: November 11, 2024

a = 16.8247

b = -0.0073

s = 0.1512

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × -0.0073) – 1

= -93.10%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.1512) – 1

= 83.11%

#### June 13, 2024 calculations

Top border of price channel:

Exp(Y_{1,153})

= Exp(a + b × X_{1,153} + 2 × s)

= Exp(a + b × 1,675 + 2 × s)

= Exp(16.8247 + -0.0073 × 1,675 + 2 × 0.1512)

= Exp(4.8579)

= $128.75

Bottom border of price channel:

Exp(Y_{1,153})

= Exp(a + b × X_{1,153} – 2 × s)

= Exp(a + b × 1,675 – 2 × s)

= Exp(16.8247 + -0.0073 × 1,675 – 2 × 0.1512)

= Exp(4.2529)

= $70.31

#### November 11, 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(16.8247 + -0.0073 × 1,826 + 2 × 0.1512)

= Exp(3.7518)

= $42.60

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(16.8247 + -0.0073 × 1,826 – 2 × 0.1512)

= Exp(3.1469)

= $23.26

#### Description

- The secondary trend is decreasing.
- The decline rate of the secondary trend is 93.10% per annum.
- SMCI price at the close of November 11, 2024 was lower than the bottom border of the secondary price channel by $0.03 (0.14%).

- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.

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