# Arch Resources Inc (ARCH)

Arch Resources, Inc. produces and sells thermal and metallurgical coal from surface and underground mines. The company is headquartered in St. Louis, Missouri.

## 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 13.44% per annum.
- ARCH price at the close of October 4, 2024 was $138.18 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 33.28% per annum.
- ARCH price at the close of October 4, 2024 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.

### 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 ARCH 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 2, 2022

End date: October 4, 2024

a = 4.4219

b = 0.0003

s = 0.1211

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0003) – 1

= 13.44%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.1211) – 1

= 62.31%

#### March 2, 2022 calculations

Top border of price channel:

Exp(Y_{605})

= Exp(a + b × X_{605} + 2 × s)

= Exp(a + b × 877 + 2 × s)

= Exp(4.4219 + 0.0003 × 877 + 2 × 0.1211)

= Exp(4.9671)

= $143.61

Bottom border of price channel:

Exp(Y_{605})

= Exp(a + b × X_{605} – 2 × s)

= Exp(a + b × 877 – 2 × s)

= Exp(4.4219 + 0.0003 × 877 – 2 × 0.1211)

= Exp(4.4828)

= $88.48

#### October 4, 2024 calculations

Top border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} + 2 × s)

= Exp(a + b × 1,824 + 2 × s)

= Exp(4.4219 + 0.0003 × 1,824 + 2 × 0.1211)

= Exp(5.2944)

= $199.21

Bottom border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} – 2 × s)

= Exp(a + b × 1,824 – 2 × s)

= Exp(4.4219 + 0.0003 × 1,824 – 2 × 0.1211)

= Exp(4.8100)

= $122.73

#### Description

- The primary trend is increasing.
- The growth rate of the primary trend is 13.44% per annum.
- ARCH price at the close of October 4, 2024 was $138.18 and was inside the primary price channel.

### Secondary Trend

Start date: January 3, 2024

End date: October 4, 2024

a = 6.9022

b = -0.0011

s = 0.0640

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × -0.0011) – 1

= -33.28%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0640) – 1

= 29.16%

#### January 3, 2024 calculations

Top border of price channel:

Exp(Y_{1,067})

= Exp(a + b × X_{1,067} + 2 × s)

= Exp(a + b × 1,549 + 2 × s)

= Exp(6.9022 + -0.0011 × 1,549 + 2 × 0.0640)

= Exp(5.3131)

= $202.97

Bottom border of price channel:

Exp(Y_{1,067})

= Exp(a + b × X_{1,067} – 2 × s)

= Exp(a + b × 1,549 – 2 × s)

= Exp(6.9022 + -0.0011 × 1,549 – 2 × 0.0640)

= Exp(5.0572)

= $157.15

#### October 4, 2024 calculations

Top border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} + 2 × s)

= Exp(a + b × 1,824 + 2 × s)

= Exp(6.9022 + -0.0011 × 1,824 + 2 × 0.0640)

= Exp(5.0082)

= $149.64

Bottom border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} – 2 × s)

= Exp(a + b × 1,824 – 2 × s)

= Exp(6.9022 + -0.0011 × 1,824 – 2 × 0.0640)

= Exp(4.7524)

= $115.86

#### Description

- The secondary trend is decreasing.
- The decline rate of the secondary trend is 33.28% per annum.
- ARCH price at the close of October 4, 2024 was inside the secondary price channel.