# 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 105.14% per annum.
- ARCH price at the close of May 24, 2024 was $170.60 and was lower than the bottom border of the primary price channel by $126.53 (42.58%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 18.31% per annum.
- ARCH price at the close of May 24, 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 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 9, 2020

End date: March 10, 2023

a = 2.4245

b = 0.0020

s = 0.1595

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0020) – 1

= 105.14%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.1595) – 1

= 89.25%

#### March 9, 2020 calculations

Top border of price channel:

Exp(Y_{197})

= Exp(a + b × X_{197} + 2 × s)

= Exp(a + b × 286 + 2 × s)

= Exp(2.4245 + 0.0020 × 286 + 2 × 0.1595)

= Exp(3.3065)

= $27.29

Bottom border of price channel:

Exp(Y_{197})

= Exp(a + b × X_{197} – 2 × s)

= Exp(a + b × 286 – 2 × s)

= Exp(2.4245 + 0.0020 × 286 – 2 × 0.1595)

= Exp(2.6686)

= $14.42

#### March 10, 2023 calculations

Top border of price channel:

Exp(Y_{954})

= Exp(a + b × X_{954} + 2 × s)

= Exp(a + b × 1,382 + 2 × s)

= Exp(2.4245 + 0.0020 × 1,382 + 2 × 0.1595)

= Exp(5.4639)

= $236.02

Bottom border of price channel:

Exp(Y_{954})

= Exp(a + b × X_{954} – 2 × s)

= Exp(a + b × 1,382 – 2 × s)

= Exp(2.4245 + 0.0020 × 1,382 – 2 × 0.1595)

= Exp(4.8261)

= $124.72

#### Description

- The primary trend is increasing.
- The growth rate of the primary trend is 105.14% per annum.
- ARCH price at the close of May 24, 2024 was $170.60 and was lower than the bottom border of the primary price channel by $126.53 (42.58%). This indicates a possible reversal in the primary trend direction.

### Secondary Trend

Start date: February 28, 2022

End date: May 24, 2024

a = 4.2376

b = 0.0005

s = 0.1139

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0005) – 1

= 18.31%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.1139) – 1

= 57.71%

#### February 28, 2022 calculations

Top border of price channel:

Exp(Y_{695})

= Exp(a + b × X_{695} + 2 × s)

= Exp(a + b × 1,007 + 2 × s)

= Exp(4.2376 + 0.0005 × 1,007 + 2 × 0.1139)

= Exp(4.9292)

= $138.26

Bottom border of price channel:

Exp(Y_{695})

= Exp(a + b × X_{695} – 2 × s)

= Exp(a + b × 1,007 – 2 × s)

= Exp(4.2376 + 0.0005 × 1,007 – 2 × 0.1139)

= Exp(4.4736)

= $87.67

#### May 24, 2024 calculations

Top border of price channel:

Exp(Y_{1,258})

= Exp(a + b × X_{1,258} + 2 × s)

= Exp(a + b × 1,823 + 2 × s)

= Exp(4.2376 + 0.0005 × 1,823 + 2 × 0.1139)

= Exp(5.3050)

= $201.34

Bottom border of price channel:

Exp(Y_{1,258})

= Exp(a + b × X_{1,258} – 2 × s)

= Exp(a + b × 1,823 – 2 × s)

= Exp(4.2376 + 0.0005 × 1,823 – 2 × 0.1139)

= Exp(4.8494)

= $127.67

#### Description

- The secondary trend is increasing.
- The growth rate of the secondary trend is 18.31% per annum.
- ARCH price at the close of May 24, 2024 was inside the secondary price channel.